Since freedom of speech has long been interpreted as freedom of expression (as it should be), lap dances fall under it. Although assembly could be tied into it as well.
I think they would have trouble banning lap dances in general, however I suspect that they can ban them as a service done for a fee.
They can't ban sex, but they can ban prostitution, and I would think that this would be similar.
I think doing so is a waste of time, but I don't see why South Carolina shouldn't be able to ban it.