The singer will feature on the US rapper's new cut 'Partynauseous', which will be released on September 6, and has admitted that the track relates to her troubles with Jakarta.
"I wrote "PARTYNAUSEOUS" about Jakarta, and my relationship with that country," GaGa tweeted. "Wishing I could "get high with the enemy" and make peace.
"Once @kendricklamar + I started talking about life + his forward thinking views about love + hip hop the song became something more," GaGa added.
Lady GaGa was forced to cancel her 'Born This Way Ball' show at the Gelora Bung Karno stadium on June 3 over security fears.
Groups including the Islamic Defenders Front (FPI) had threatened violence if the singer went ahead with the show, claiming that her revealing outfits and provocative dance moves would corrupt the country's youth.
Meanwhile, GaGa will release her third studio album ARTPOP in spring 2013, with a formal announcement due next month.
Watch the music video for Lady GaGa's 'Just Dance' below: