no idea if it was "cheating", but it's more a matter of why he'd pay quite a bit of money to go off and see, at the very least, a stripper, in private. I'd probably bite my lip and accept it if it was a stag do, same as a night with the Chippendales; but a private performance? Why was he there? What did he want?
Whether it's a dumpable offence is up to the offended party. Would you fancy continuing a relationship, maybe even marriage some day, with a guy who pays lapdancers? Or do you think it's something he'll grow out of?