Still, it makes sense
In English, the adjective meaning "of or about the Moon" is already lunar.
Even so, I think it's just waaaaay too soon to worry about the semantics of capital-M Moon (Earth's) versus small-m moon (everyone else's). If four decades of SF reading provides any insight, it will only be after humans live in other solar systems that they'll call their star "the sun" and Earth's sun Sol. They'll call their moon(s) by whatever name the original expedition gives them, and they'll probably call Earth's moon Luna, if they refer to her at all.
All presuming (as SF always does) that English is the sole language used by all humans who emigrate to other worlds... I realize the same thing happens to sol as to luna in Romance languages.