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One kiss, Lucifer promises, and Sam will never again feel how cold they both are. Two, and he will forget Dean and everyone he's lost, never to hurt again.
"And three?"
"Three would kill you," Lucifer says. "I will not give you three."
That's what undoes him, to keep Sam rather than kill him. He never considers that Sam's kisses may have power, too. That if he lets Sam close to the ice in his heart, Sam's tears will melt it, and Lucifer will see all the beauty in the world again.
And the first thing he sees is Sam.