Kitty, 27, was recently kicked out of the show after ending up in the vote-off with Misha B.
The judges then decided to send Kitty home rather than Misha. Lady Gaga is one of Kitty's idols and she had performed on the show earlier that evening.
Gaga then comforted Kitty by running on stage and giving her a hug.
A source said to UK newspaper The Sun: 'Gaga couldn't believe Kitty has been axed and thought she was one of the most talented and exciting acts in the competition.
'She thought Kitty had been misunderstood and it reminded her of her own struggles to be accepted.'