Only if they are doing complicated choreography. If they're doing some one step two step simple dancing then they should be singing live because that doesn't exert a lot of effort. If they're dancing at a professional level then it's better to lip sync because if they don't they'll be out of breath and it won't sound that great. Dancing (hard) and singing live at the same time is extremely difficult and only a couple people can pull it off.
I have more respect for the artist who sings live and doesn't sound so great than I do the bitch who just stands up there and lip syncs the whole time.
If you're famous for your vocals such as Adele, xtina then no you shouldn't lip sync. But if your known as a performer, I don't see the problem with lip syncing.
Yes, nothing stipulates that they have to sing live. I will say that when Celine/Mariah do it its worse than if Britney does it because they are vocalists.
