Sorry you're here. I'll try to keep this short and simple.
Your need to know the truth will not serve you well here. What will knowing the truth do for you? If you need to know because he may be crossing boundaries, i.e. not calling/receiving calls from OM, then you may as well just assume he is already doing that.
For most of us, myself included, this need to know is related to our need to control the situation. You cannot control this situation. You CAN, however, set and enforce boundaries, but if you are going to do that, you have to follow through.
You said you "gave him your marriage boundaries" but then you said he crossed that line, right? Now what? What was your stated reaction going to be when he crossed the line? Did you do that?
My point is that while boundaries are almost a necessity in our sitches, one that is pretty hard to set and enforce is the "no OP rule". If it were that easy then the affair would probably not still be going on. Also, I would assume that your H already knew that sleeping with another woman was a boundary of yours but now that he crossed that line, and you're still there, it's pretty hard to say "ok, you crossed the line 4 times already, but that 5th one, well, that's the last straw mister!"
As far as the lying goes, well, again, that's why the "no contact" boundary, at least at your stage of the sitch, is a really hard one to put in place. You CAN do it, but it's akin to the "me or her" ultimatum and as such, is not really advocated by DB.
DB suggests that we not focus on the affair. We don't snoop, or try to figure out our WAS. We simply turn our attention/energy towards ourselves and do work that WILL have a positive effect on our lives. I think if you give this some time, time spent on you and letting his C work, you may see some positive results. (BTW, are you seeing a therapist?)
Anyway, he WILL lie some more, count on that, but what you do not know, and I don't care how much you snoop, is what the lie really is. Is the lie simply that he's in contact with her, but your mind is filling in the rest, i.e. the PA is still in full effect? Or maybe is the lie that they are in contact but he's trying to break things off? Maybe the lie is that he's still in love with her but knows your marriage is more important and he's struggling with that fact. Then again, the lie could be that it's still a full blown PA.
Worrying about what he's doing, and what he MAY be lying about is not going to really do much for you. He may continue to lie once the A is breathing it's last breath, but in that case motivated more by a desire not to hurt you than getting away with something.
I am not trying to paint a optimistic picture for you, although there COULD be the chance that it is. What I am trying to tell you is that all you THINK you know is likely only part of the truth at best and no matter what, you're best served doing the ultimate 180 and just working on you, allowing him the time and space he may need to get his $hit together.
