I'm pretty convinced that she's Ni-dom. I have seen several interviews in which she talks about her creative processes. It sounds to me that her creative ideas are usually totally random and out of nowhere. For instance, while she was partying in Amsterdam, it occurred to her all of a sudden that she wanted to give birth to her own head in the Born This Way video. Also, we all know how much she's obsessed with metaphors, which might indicate heavy use of Ni.
I don't see Fi-dom or even Fi-aux in her, because she gets defensive quite easily when criticized. The piece she wrote for V magazine was basically a defense against the plagiarism accusations, which I think was unnecessary.