They've been together in the same room at least four times today without
either one being upset. No growling, no hissing. In fact, at one point I was
holding both of them in my lap and both were purring.

There may yet be hope!

I don't know why their enmity developed in the first place. When Billy &
Lily first came to live with us, Eli LOVED Lily to pieces and the feeling
was mutual. Hopefully they can soon get back to being in love.