Personally, I wouldn't class a lap dance as cheating. However, I would find this behaviour deeply unattractive, and it could end the relationship as a result.
If he only had a lap dance because all the other blokes egged him on - well, that makes him susceptible to doing all kinds of crap because the lads said to. I find that mentality a huge turn off. I want a partner who makes sensible decisions based on what feels right to him.
If he had a lap dance because he didn't see the harm in it - well, he didn't consider how I would feel, knowing he'd been sexually aroused in public by some woman who probably looked nothing like me. I'd feel less than. I don't want a partner who makes stupid decisions without considering my feelings.
If he spent shared money on it rather than his own money - I'd feel disrespected. I'm fine with a man watching porn etc, but I find the idea of paying for it repulsive, and the idea of using my money even more disgusting. I guess a tenner out of his own funds for a pay per view video when staying in a hotel room by himself wouldn't get me, but the amount of money, and the amount of live interaction would. Something pre-recorded by some girl he's never going to see in real life is a fantasy. A woman gyrating in his face in real life (or even webcaming him) crosses that line between total make belief and reality. Don't men have any imaginations?
So... in short, I guess what I'm saying is, it doesn't really matter what label you stick on it. A lot of women, even if they wouldn't consider it cheating, would consider it unacceptable.