Lucifer not being able to hurt or kill sinners makes him make so much more sense!
Like, he literally can't DO anything about them, and he's stuck with the worst of them. Can't get away, can't get rid of them. Of course hes gonna get depressed. Of course he's gonna isolate.
He has no clue what is going on in hell, by choice. He doesn't meet with the sins, doesn't go to court, doesn't actually rule. He doesn't pay attention to the news because he doesn't want to know.
Instead he goes full on into escapeism. Locking himself up in his room, obsessively focusing on his ducks, ignoring the world outside because he just can't DEAL with it, both literally and metaphorically. He's stuck, and he takes ignoring the sinners to the next level.
The only thing that can break him out of this is his family. He only actually is like, fully emotionally present for Charlie and Lilith, he just doesn't care about anything else.
Both in the fight with Adam and Vox, he only goes to his full form when he actually is emotionally involved, when he's actually pissed off. When the snake goes from his hat to his horns and his eyes go full on red, which is both times when his family gets involved. All the things he says to Vox before, thats just drama, not actually him.
Give that man a therapist, an emotional support animal and a vacation away from hell. He needs it.