Not really a problem if she did. If Azealia sent her a beat and she wrote over it but wants to keep what she wrote and re-create an instrumental with one of her other producers that's not illegal.
So Azealia basically just revealed that the collabs were never a thing, and that she sent demos to Gaga? Like when she "worked with Beyonce" and it was actually just her trying to get Beyonce to record the song "ATM Jam"?