He's still involved with OW and can't give her up.
The most important thing: You need to Get a Life. Do things for you. This whole affair is sucking up all your energy. Become interesting, joyful, fun and sexy. This will help you to survive if he really leaves for good and...it will be the only thing that brings him back.
The affair may need to play itself out, but you need to become more interesting than OW.
Of course he's lying. Being "in love" is a form of psychosis. He can't think straight.
Even if her wanted to break it off...Breaking it off with the OW is like trying to quit drinking. There are backsliding experiences. He's addicted.
You have a better shot of him seeing your changes if he's still at home. You have to decide if you can function well while your husband sleeps with a good friend of yours. Some people can, some can't.