It depends on the indiviual but no, that's not cheating. I don't see how it would be, he's not doing anything wrong.
Clubbing is just clubbing and he's only lying IF YOU ASKED and he said he wasn't going but he really did.
If he goes somewhere and doesn't tell you in advance there's nothing wrong with that, he's his own person afterall.
My bf always tells me where he's going but that's only because we live together. If we didn't he probably wouldn't and I wouldn't ask because I don't have to know where he's at 24/7.
As for dancing with another person, it's just dancing. Of course if he's grinding his piece into some girl then yeah, I'd be annoyed but I'd talk to him about it and tell him how I feel. It's not something to break up over if you're in a mature relationship.
My bf goes clubbing with his friends almost every Saturday (his BFF is single and lives alone, the guy gets lonely). I never go because I'm not the clubbing type and I can't stand the music they play.
But I trust my bf and knows he wouldn't do anything to disrespect me and yes, I'm fully aware he'll be dancing with other girls because I see the pictures afterward, usually. It's all harmless and most of them are his female friends I've met (who have bfs of their own).
Guys don't like clingging women. Hell, women don't like clingging men.
Just because you're with someone doesn't mean you own him/her, you guys are still two separate people with your own lives.
That's something not many people understand and it leads to unnecessary drama and breakups.