He would, in fact, play the game properly, truth and all. He needs to find a way to crack into her psyche, after all.

"It is awfully cold here," Lucifer says, only the barest hint of mockery, rolling his eyes to indicate the building. Unfortunately for her, he knows what it is supposed to be like, not these odd glitches that keep flicking through it. "But Hell burns far hotter than myself," he adds, pressing his thumb into the bartop and a slow frost spreads from the touch, forming a small circle from the radius. He doesn't let it continue, however, and pulls his hand back.

Honestly his own natural cold and his weakened form and the chill of Thorne has been a really terrible combo.