Lucifer isn't in possession of another jacket and he feels the cold fiercely here, which means he doesn't offer his jacket, but he does press in close to the detective, wanting to share warmth as much as he can.

"Here," he says, and reaches out for her hands, because he doesn't need a jacket to warm her up. "I can warm your hands, but I am not drinking moonshine," he says, with a cringe and a scoff. He'd say when hell freezes over, but clearly the devil is about to freeze over if he's left out here in the cold much longer. "The fireplace and hot cocoa will have to do," he allows. "Until I can find a proper top shelf."

And yet, he's still rather proud of the humans. You stick them in one of Dad's little hole-in-the-wall traps and they get right to figuring out how to endure using alcohol. It's like a page out of his own playbook.