It already took untold amounts of official permission and blessing to get Lady Gaga's likeness onto The Simpsons--or, more specifically, multiple likenesses. Once you've cleared that hurdle, why not get Gaga to perform a song while she's there? Of course she did. This is silly talk.
That song's called "You're All My Little Monsters," Gaga sang it herself in voice-over and it's more or less a Stefani Germanotta pastiche, or perhaps like "Born This Way" without the specific messages or half its instrumentation. Specifically, the first part of this is very Jason Robert Brown and the second is Jason Robert Brown with a tinny, latter-day Kylie Minogue beat grafted on. (The sexy-mister-Hyde version of the song, you might call it. That single phrase is more Gaga than anything else in the pastiche.) It goes without saying that we prefer Born This Way, but this is the new music we've got, and at least Gaga's got the piano-backed background to pull it off. The episode aired last Sunday; here's the song portion.