I am guessing that the feed from the mic is not the one being fed to the audience, but she simply sings along anyway since it might be more difficult to lip synch, meaning she gets more into the show and her dancing by actual singing. But considering her shows obviously center around the dancing and whatnot on stage, it is no surprise that she would be out of breath singing (as most of us would).
In other words, she is not lip synching, per se, but a pre-recorded track is what the crowd hears. I don't see the problem with that, since no one wants to hear an out-of-breath singer. This feed here was probably leaked on to the 'net by someone in her camp.