It appears Madonna and Lady Gaga have made up.

The fresh Academy Award winner and the Material Girl embraced at Madonna’s post-Oscars party, signaling an end to their long feud. A feud started in 2011 after Gaga was accused of ripping off Madonna’s 1989 song “Express Yourself” in her single “Born This Way.”
Gaga criticized Madonna for not voicing her issues directly in the documentary “Gaga: Five Foot Two”:

“The only thing that really bothers me about her is that I’m Italian and from New York …so if I have a problem with somebody I’m going to (expletive) tell you to your face.”
She said in the film. And she continued:
“No matter how much respect I have for her as a performer, I could never wrap my head around the fact that she wouldn’t look me in the eye and tell me that I was reductive or whatever. … Telling me you think I’m a piece of (expletive) through the media?”
But we can say the argument ended positively, after all.