This is slightly incorrect. Lich implies the existence of a phylactery. This post says that it binds its soul to an animated corpse but this is inaccurate. It has to be an inanimate object, for instance, a box or a cup, or a crystal. So, we would have to look for what that object might be. It can’t be the cross because he didn’t see it before that day. I postulate that it’s the Holy Grail.