The Lunar Empire is the name of the kingdom under Nightmare Moon's ruling in one of the Alternate Timelines - the one presented in Butterfly Wings.
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The Lunar Empire as a whole mirrors that of Equestria in the true Timeline, with a few exceptions. Namely the Castle of the Two Sisters being fully restored and in pristine condition. It was first established when Celestia lost her life to king Sombra as a response to the kill, and the new responsability Luna had to face.
Not too much is explored in the empire's workings; Nightmare Moon made it clear that, due to the current war occurring, no creature stronger than Nightmare Moon is allowed to live in the Lunar Empire, due to the possible risk involved in a spy entering the kingdom.