I don't think the question of "did Lady Gaga rip off Annie Lennox" is a useful or even valid one.
For one thing, "it's only culture if it's shared" as Cory Doctorow says. For performers and artists, it's not merely legitimate to be inspired and influenced by previous artists and their work, it's pretty much how artists learn to do art and be artists. "You have to know the rules before you can break them" is one way of putting it. It's one of the reasons that beginning artists are encouraged to reproduce works of art by previous great artists — that's how you learn how to do it. They do it at the Louvre and other museums. Even Norman Rockwell depicted it.
For another thing, was Lady Gaga's "Jo Calderone" persona making reference to Annie Lennox's "Earl the Rocker" character at the 1984 Grammy awards? To my eye, almost certainly. But both of them are making reference to Elvis Presley and Sal Mineo.
So, to make use of the "generic all-purpose Buddhist response to criticism or voices of self-hate" that Cheri Huber recommends: "Lady Gaga 'ripped off' Annie Lennox? Whatever."