I can understand the comparisons, both started out with their own name before flopping and both came back with a new label and a new image. And both have this secrecy surrounding them (not so much for GaGa anymore, which I think is why she hasn't been as successful this go around).
But honestly, I don't think LDR wants to be the next GaGa. Nothing about her live shows screams musical theatre quite like GaGa.
A more apt comparison would be Katy Perry, especially looking at Katy's early days. I can only hope her albums are less pop than OOTB an TD.