I would suggest you leave. I have been in a few relationships like this and it is not worth it. I stayed with someone after I found out they were cheating and they never changed, I had a fear of being lonely but instead I hurt more than ever.

He doesn't sound like a sex addict he sounds like a cheater, and liar. The therapist even said most people would have left.

Has he talked to any other girls since you both have been to therapy?
What is it that you like about this guy and the relationship?
Are your needs being met?
Why do you choose to stay?