As far as I know, Lady Gaga hasn't written any fugues. She may not even know what a fugue is... Do you?
Giovanni Dettori's Lady Gaga Fugue shows you what a fugue is and, if you read music, you can follow along as you listen. It is based on a part of the song Bad Romance
Do you notice how the tune from Bad Romance keeps coming back in different ways? It takes a lot of skill to write a fugue. Giovanni Dettori teaches people about counterpoint, which is the discipline of writing a piece of music that has several tunes going at the one time. Sometimes, as in a fugue, the tune is being harmonised with itself.
Composer, Giovanni Dettori has kindly published the sheet music for you to download and play as a free pdf file.