Correct. It is not in contention whether Lady Gaga had a sex change op. or whether she identifies solely with the opposite sex (Clearly she enjoys being female or at least utilizing that sex instead of desiring/acting male).
Now, she might be a hermaphrodite...
I saw a tv show clip one time with Lady Gaga on it, and she mentioned sleeping with her boyfriend, but she didn't go into much detail. I suppose that still doesn't say much about whether she's a girl or a guy (or both).