If I divorced my stbx for a lie, I would have divorced him almost every time he opened his mouth. There must be more going on and you should talk to him. People make mistakes. I don't know what you lied about but its hard to believe a lie would be the end.
Please hang in there. I know its rough right now, Im there too. It hurts like heck but I have faith that one day I will be happy again. post here for support. make some new friends. We are all here for you .