To begin with, Elizabeth gets Elda's Christmas card (featuring her and Toushiro because it was taken before Silver and her had fixed things up entirely) so there's that.

In terms of an actual gift Elizabeth is going to get earrings (Silver, custom-made to her best approximation of Thanatos's face from memory of that dream dangling off the ends of them) custom-made for her. And then also a pair of tickets to that Anastasia musical that's in town. You know, if she wants to take anyone there.