I was compiling Mythologies info for my planned chronology last week, and yeah, Lucifer is mentioned as the Netherrealm's previous ruler. He tormented Shinnok for millennia until the latter made his deal with Quan Chi; after they eventually took him down, Shinnok imprisoned Lucifer's essence.

While I think it'd be a little too...obvious...to just bring him on board as a playable character, I think it'd work quite well if he was introduced under a completely different name and guise, and have the reveal take place in his ending.

I would rather not have half-assed non-catechetic interpretations of contemporary religions in my games.

There actually isn't a Lucifer, because Lucifer comes from the Latin word used to translate the Hebrew word heileil, referring to a "day star" or "morning star". It's used in a verse in the Book of Isaiah that refers to Nebuchadnezzar, a wicked Babylonian king. It has nothing to do with Ha-Satan, who is actually a servant of YHWH, not a fallen angel who wants to overthrow him. He acts as a prosecutor who acts as a challenge for humans to overcome in order to become closer to YHWH. Essentially, Ha-Satan is a metaphor for the evil impulse that YHWH gave to humans in order for them to have the potential to grow.

Of course, it would probably just be easier to use the Christian version of Satan. Either way, I don't know if using Satan would be a good idea unless perhaps you were trying to do some kind of spoof of biblical stories.