So she copied exactly what Madonna did 26 years earlier.
Well, it's not like she's a messiah or anything... She's a pop singer that's performing in the pop world. Everything has been done before. She's just smart enough and has enough business/marketing sense enough to take a direction that she knew that would be successful.
The big difference with her then Madonna and some of the other pop stars is that Lady Gaga actually really knows music on a technical level, and pretty much single handedly crafted her persona. Madonna's wierdness was later in her career, and shaped a whole lot by suggestions of a marketing team. For the most part, Lady Gaga started out as more typical jazz/theater/rock singer as a music student, but then said 'screw it, I wanna shoot for the moon with something over the top.' She succeeded.