You're not gonna get that demon. If its exorcised its down in the pit and its one of a million again. If you had a name you could summon it but one way street sadly. Its down there, probably very proud of itself but still hating hell. Always hating hell. And there's probably a few demons out looking for chances to possess some of you, there's also the crossroads whores, the ones out to tempt and then there's the bigger more dangerous ones.
Its not just so simple as bad demon take over mind. Play games. Go home.
One thing I will say as someone who has played the possession game over and over. We get in a head we know everything. Every thought they have every single bit of knowledge. So whatever Chloe knows, Lucifer will be more than aware of already. And there's your reason. It wasn't that it was her, it was that it was someone from the lot of you. Someone who didn't have the amulet and someone an opportunistic demon thought hey, reason. Probably one topside already that jumped bodies.
Side effects, none really. She's lucky it didn't ride her hard, she'd be dead, but depends how long it was in there. It was obviously recon more than anything else.