Hi. It is the lying rather than the act. I went through something similar and while the lapdance was shit the thing that really caused the big issue was the fact my husband had always been so anti lapdancing....To the point he had steered stag dos in different directions etc. I found out about it by accident....And my husband just assumed our marriage would be over.
My best friend happened to be at a party my husband went to immediately after it. Before I found out about the lapdance my friend had asked if my dh was okay because he was so drunk and unhappy at the party.
My husband had gone out with his arsehole pal who was splitting up with his wife. My stupid husband got ratted and this idiot friend took him into this lapdancing club.
It shook the foundations of our marriage. Weirdly it was only my husband who got that it was a deal breaker. My dh was the only one who got why i was so upset/angry/hurt. There was a lot of minimising among friends and family, or at least the few I spoke with.
I think the reason I got over it was due to my husband's reaction to it. He went out of his way to apologise. He never sees that particular friend anymore and curtailed his drinking considerably.
One couples deal breaker is another couple's tiff. Only you know how much of a deal breaker a lapdance is. For me it was the lying or at least the omission that caused the hurt. I questioned everything I thought I knew about him.
Looking back I am glad we got over it. Our relationship was more than a drunken mistake. I love my husband as he loves me. If I were to fuck up I would want him to give me another chance. Forgiveness and understanding and love can all be very powerful. Although it is difficult/impossible to forgive if he isn't sorry.
I really feel for you. Such a horrible time. I hope you work it out.