The Collaborative International Dictionary of English v.0.48:

Lunarian \Lu*na"ri*an\, n. [See Lunar, Luna.]
   An inhabitant of the moon.
   [1913 Webster]

The Devil's Dictionary (1881-1906):

LUNARIAN, n.  An inhabitant of the moon, as distinguished from
Lunatic, one whom the moon inhabits.  The Lunarians have been
described by Lucian, Locke and other observers, but without much
agreement.  For example, Bragellos avers their anatomical identity
with Man, but Professor Newcomb says they are more like the hill
tribes of Vermont.