It is a bit unclear as to her exact origin, but it can be said that Lapis Lazuli was made as a terra-forming Gem, and for a while she used to terraform planets without thinking twice. Overtime, she is brought into Blue Diamond's court as an aristocratic messenger Gem. During her earlier years as apart of the court, she was sent down to Earth, where at the time was under the control of Pink Diamond. During her visit however, she ended up discovering White Diamond being shattered, and as such had her memory altered by the Diamond to make her believe Rose Quartz had shattered her. She flew back to her Diamond, but instead of telling her that she was shattered, Lapis informed her that Pink Diamond had "gone missing".
During one of her flights to Earth during the Gem War, she was found by Bismuth, and got herself poofed, and subsequently ended up inside a Homeworld mirror, believing to be a member of the Crystal Gems. She remained trapped inside the mirror through the end of the Gem War, where she was left behind, and recovered by the Crystal Gems at the Galaxy Warp, presumably by Pearl specifically. It is unclear to how she got her stone cracked during it all.
During her stay at the Crystal Temple, Amethyst located her in the mirror, and asked her if they were involved in any war, to which after a bit, Lapis showed her some bit of the Gem War and an idea on what it was about. She helped Amethyst understand this and backed her up when she replayed this to the other Crystal Gems. It can be assumed Pearl confiscated the mirror and stored it in her Gemstone sometime after this.
Lapis was brought back out from Pearl's stone when Steven Universe asked Pearl to help him learn about Gem culture. However, due to how little they thought of her, Lapis refused to activate for Pearl, and Steven took her out for the day where she started to bond with him. Near the end of the day, Lapis got Steven to release her from her mirror for the first time since her capture. The Crystal Gems tried to stop her, but Steven's Portal Key opened a portal to Equus, which she and Steven fell into. She ended up landing in the Castle of the Two Sisters, where she first meets the Mane Six. It was at this point when Steven went to heal her Gemstone, fully reviving her.
As there was no way to return home, Lapis stayed in Ponyville with Steven, taking time to learn about Equestria, and teaching Steven a little bit about her kind, of which he knew little of at the time. She went with the other Ponies when Rainbow Dash tried to find A.K. Yearling, and during this almost got herself captured again by Ahuizotl. She was found later by Discord, who mocks her by saying how little she truly cared for any other Gem except herself. Determined to help her friends (and to prove Discord wrong), she went right back to the others and helped them stop Ahuizotl, successful in her endeavors. Not too long afterwards, she and Steven found Pearl, Amethyst, and Garnet coming to Equestria, and learning a bit from Discord's talk, she decided to join Steven in showing Amethyst and Pearl around the place, afterwards joining the Crystal Gems back at the temple.
From there, she continued to aid them in their numerous missions and adventures on behalf of Steven mainly, including helping Steven find a cure when the group became infected by Poison Joke. During her stay, she told Steven about how Gems are made, and eventually was convinced to take him over to the Prime Kindergarten. She was found out by Pearl however, and she quickly insisted that Steven made her bring him here, saying it wasn't all her fault.
When Jasper arrived to Earth, Lapis was one of the few that stayed back during the first initial fight, mainly because she didn't want to fight her own kind, thus resulting in her capture. While she was released and got back to Earth, she was quickly apprehended by Sombra, and captured once again alongside Twilight Sparkle and Sapphire. She managed to get them out after working some of Twilight's sweat into a blade, cutting the chains that kept them down. Upon release, she aided Garnet and Twilight in fighting Tirek, but ended up getting her magic sucked away. Luckily this didn't last too long and she returned once Tirek was defeated. After the fight, she helped Connie Maheswaran and Her Parents back home.
Lapis Lazuli continued her stay on planet Earth, rather than try to get herself home, and it was during a mission to the Prime Kindergarten that she found out through a messaging device that Blue Diamond still had her positions open for both her and Sapphire. She discussed this sometime later with Garnet, and was the first to find out about Garnet's vision of friendship on Homeworld, which she was more than happy to take part in creating the Galactic Ray. As they were doing that however, a Jet Monster arrived on the scene, and managed to capture her, Peridot and Diopside. They tried to get themselves out, and they only managed to once she and Peridot fused, aiding Carnelian in finishing off the Corrupted Gem.
During production however, Lapis found Steven was grounded to Earth, Greg Universe not allowing him to go. Trying to cheer Steven up, she snuck him out that night and got him to try out a Robonoid, though being caught by Kyra later on that night.
Homeworld Arrival Arc
Joining the others, Lapis Lazuli left Earth behind and arrived to Homeworld, where she was warmly welcomed back by Blue Diamond herself. She resided in the main palace during her stay, and as she was, she went with Sapphire and Rarity in order to check out an Abandoned Gem Settlement, in order to figure out why it had been abandoned. During their search, Lapis and the others located an Angler Monster inside, which almost killed them in their escape from the settlement.
Upon the Osicone's return, she joined the Gems in fighting it head on, insisting that Steven and the Ponies stay behind to be safe.
Her involvement in Season 3 is fairly small, her being more of a side character to the events occurring, which included helping in Cranky Doodle and Matilda Doodle's wedding, and her body swapping with Fulgurite for a limited time.
Upon seeing Stevonnie, she immediately decides to have fun with her and hang out with her for her birthday, and Lapis's own anniversary being celebrated on the same day. Amongst the activities included visiting Ponyville, playing together in a nearby pool, and even watching a movie together before Flint found them. She and Stevonnie got him off their back, her saying she found a Gem object for him to take back as they snuck off to join The Cool Kids at a RAVE. They had their fun, although running into some trouble with Kevin, before the night was over. Sometime later, as a thanks, Steven, Connie, and Peedee Fryman tried hooking her up with Ronaldo Fryman, which didn't work. Sometime later though was when she first met Jamie, already finding him interesting and enjoyable.
Sometime later, as she was playing with Steven by the shores of Beach City, she ended up coming across a Coelacanth, and immediately got Steven and Jade to come on a underwater expedition. The expedition lead her to the Time Temple, where she and the others found what they assumed to be a Time Hourglass inside, and tried to use it to bring the Coelacanth home. Instead, it brought them to a water Temple within Equus, and discovered Warp Pads were evident in Equestria as well.
When Bismuth made her return, she and some others were told to stay at the Barn House until they think Bismuth would be ready to handle how much had changed. However, she snuck in on Bismuth's training, revealing just how bitter she was towards her and explained how she got stuck in her mirror in the first place because of her. When the group went to the Heart's Warming Eve festival in Canterlot, they tried to get Lapis to warm up to her, but Lapis didn't believe it was going to happen, but did at least give Bismuth a small present once the event was done as a starting point.
Season 4 Finale
Upon hearing of Sapphire's capture, Lapis joined the whole team in heading to the White Diamond Space Station, her taking the role of the leader of the group sent to Earth to retrieve some more Humans for the Human Zoo, assigned by Flint. She managed to convince them to let the group in, and once she did that, she split off in her own group to rescue Steven, Connie, and the Mane Six from the Human Zoo. She got them out, but in their run to get out, she and the others ended up in the Science Chamber, where sometime later White Diamond herself took them hostage. She was brought to the throne room, and after a while got free from her restraints. However, once the duel between White Diamond and Earthstone happened, Lapis intervened and got her gemstone severely damaged, driving her into a blind rage. She poofed White Diamond, and went to attack everyone else in her rage state, when Jasper came in and forced her to fuse with her, forming Malachite, and making her and Jasper fall from the space station down to Earth.
Lapis Lazuli isn't too involved throughout Season 5, mainly because she stayed trapped as Malachite. She was eventually healed, and freed from the fusion, but once she returned, re spent the remainder of the season isolating herself inside the Barn House, blaming herself deeply for what happened, and thinking herself as a terrible Gem for it.
Lapis is shown to seemingly have recovered from her Malachite experience, and has returned a new form and enjoying herself again. During the start of the Pink Diamond case, Lapis was brought to the killing site that was Pink Diamond's Palanquin, where she reveals that she did see something happen there, but claims she wasn't sure exactly what entirely, just knowing that Pink was shattered there. Before the Summer Sun Celebration, Lapis arrived in Canterlot with the others, just to hear word of Solitaire's upcoming attack on Canterlot. She and Blue Pearl went to investigate, only to find out that Solitaire was blind. This gave her the idea to bring Luna and Celestia to him, and helped him regain his sight.
She eventually became one of the Gems affected by the Tantabus, though it wasn't clear if it did affect her dream or not. When all the dreams came together, she tried to fight the Tantabus, but it took the form of Malachite, and she ended up feeling guilty and distraught all over again. This similar behavior went on as she was helping build Connie II's new home, something she tried to keep to herself for the time being. During this some time later, she was found by Pearl, and she found out how much Pearl had to go through. She allowed her to stay with her, and this resulted in Spinel. When they checked inside Spinel's head, Lapis thanked Pearl for fusing with her, as she found someone who actually understood what she was going through, and how this fusion wasn't hurting anyone either.
She remained as Spinel for sometime afterwards until she and Pearl decided to unfuse themselves, and just in time as she and the others were ready to question Pearl. She and Bismuth both tried to help Pearl with her issue, but found she didn't have control over her silence, and she ended up poofing herself. Lapis ended up captured by White Diamond again soon after, but was rescued by some of Steven's human friends.
After crash landing on Jungle Moon, she and everyone else travel amongst the planet, and eventually took their refuge inside the Jungle Moon Base, awaiting for the Diamonds to rescue them. During this stay on the Jungle Moon, she and Bismuth had to go and gather more food for the Humans and the Ponies. Also during this, it is revealed by Tiger's Eye that prior to White Diamond's capture, Lapis, Bismuth, and Tiger's Eye went to the Prime Kindergarten on a Gem mission. Lapis still felt extremely bitter at Bismuth for what she did to her back at the Gem War, to the point when Bismuth fully confronted her about it, she demanded that she'd simply leave her, to which she went off on her own. After an encounter with the Injector Monster however, and finding a better understanding with Bismuth, she began giving Bismuth a chance at her friendship.
She remained on Earth with some of the other Gems. During this, she went with Applejack and Peridot into Klugetown. During there, she and the others discovered their Portal Keys within a auction set up by Verko. She tried to just take them back, but not only was she denied, but she and Peridot were targeted by the townsfolk as merchandise, people wanting to buy them off. Eventually she came up with a plan to give herself and Peridot over to Verko as a trade, only to reform in his office and successfully stealing back their Portal Keys.
Pink Diamond Arc
After learning about the revelation of Pink Diamond, Lapis Lazuli fled to the Earth Moon Base, no longer trusting the Crystal Gems, and unsure if she should believe them anymore. She was found there by Fluorite's components, and with their help manage to convince her to come back home, seeing just how much she had done without knowing any of this. She returned in full with Bismuth, Jasper, and Diopside over to the Barn House, meeting with Peridot to make her feel better.
In Tale-Wind, she participates in the Inter-Species Race alongside Sapphire and Rainbow Dash in order to retrieved Netitus. Before the race though, she overheard Sapphire and Goldstone talking, and during the third part of the race she decided to forfeit it, putting her faith in Sapphire and letting her take the race for them.
My Little Universe II
Lapis became one of the many Gems to become rejuvenated thanks to Spinel's Rejuvenator, and as such lost all of her memory over what happened to her. Upon reforming, the first thing she did was leave the Crystal Temple, not only appalled by how the place looked but also needing to handle some terraforming on her part. Her friends confronted her as she began doing so, but she made it clear how little she cared about it, and even willingly fought them when they threatened her work. She held her own against her friends for a good while until she was faced by Bismuth, who forcefully poofed her after a short struggle.
Her secondary reformation altered her personality again, but this time thanks to magic placed on her by Bray and Budgerite, her described as being passive-aggressive by Emerald, and in love with Flint much to Spinel's anger. She basically made Flint her potential boyfriend, but allowed Flint time to give her an answer on if he would accept her or not. After a week of pestering him about it, she was harshly driven off by Flint, leaving her heart-broken and fleeing Little Homeworld onto Brooding Hill. Lapis remained at the Brooding Hill for a while longer, until she was finally found by Jamie, but due to not having any memories she rejects him as well and flees, leaving him heart-broken as well. The encounter however began to help regain some bit of her memory through her headaches, though she kept trying to deny them. She then decided, with some prompting by Sapphire, to go back to Canterlot, but she kept getting more headaches as her memories tried coming back to her. She concluded that Jamie was responsible for her pain, and managed to find him, demanding he make the pain stop (only making her pain worse). It only took the desperate move of Starlight Glimmer showing her a handheld mirror that finally completely reminded her of everything, thus returning her to normal.
After her recovery, she spends the time aiding Steven in his endeavors to try and recover the others' memories. During this, she joins Connie and Steven in locating Pearl at The Reef, and during her stay learns more about Grogar's past. Feeling sorry for the ram, she agrees with the others and decides to try and reform him, her being one of the main Gems to try to teach Grogar to appreciate life - bringing him to the Blue Star Moon as a main factor. Her largest involvement was during the Bird invasion onto Beach City, in which she learns the weakness behind the creatures and that they have to accept their sins rather than fighting them off (in her case through meditation).
She joins the Harmony Gems in both the following court session to get Discord and White Diamond's magic back, and the final main battle between them and Grogar's Army. Just before the main battle in the Realm of Corners, she joins the original Crystal Gems and Elements of Harmony to take out the weapons located on Homeworld, but got caught by Grogar and forced into fighting him. She and the others tragically got shattered during the fight. Amongst the gems, she was the first to be revived by Steven, and she helps him revive everyone else in the Supreme Kindergarten. She joins them to stop Grogar's army from leaving Homeworld.