Im not sure if Bill himself would care.. The only thing he cares about is Steffy being happy. She wanted Liam so he made it happen, but Liam now messed up in his mind, so he does not care much anymore. He only cares to play nice now because Steffy wants it. But Bill has warned her about not making it more complicated. This is all in time right before or after Hope returns. No, Liam won't forgive them.
Liam will play the victim even though he set everything in motion by spending all his energy on that redheaded tramp and then kissing her. I can hear all the "how could you do this to me?" To Steffy and Bill over and over.
I don't want to see Steffy begging this punk to forgive her but I bet that is what will happen.