I'm VERY sorry for you crazy situation ...
I'm dealing with a relapsed AH who becomes a good liar when he's drinking. The only lies (that I'm aware of!!) are those relating to drinking or purchasing alchohol. We've talked about how devastating lying is and how I won't be able to trust him. He finally admitted that he lied so that we would not get in a big fight and so he would not be adding more stress on me. My thoughts: he's still lying. He lied to not get caught - period. I feel that my AH will now lie as needed everytime he's drinking ... really, why wouldn't he? When the disease is raging in his head - lying is the easiest solution.
When you stated he was "ashamed" ... he should be BUT lying and repeating behavior is simply a way for them to continue. I view your H meeting & getting stoned with her again as innocent as mine buying vodka and not drinking it ... unacceptable to me.
You know him best ... I'm simplying pulling words out of your comments. But lying has turned into an ugly monster in our marriage (of 21 years) and I don't think I can live with it anymore ...
Alanon and friends have been my best support. I wish you the BEST - BIG hugs to you!