The "Bad Romance" singer astonished reality TV mogul Simon Cowell with her requests, but they were eventually vetoed by health and safety officers. She will instead perform on the UK TV talent show this Sunday surrounded by scantily clad male dancers.
A source said: "Simon wanted her on the show because he knows she will put 110 percent into the performance.
"She is always way out there with her costumes and dance routines. But not even he was prepared for what she had in mind.
"He thought the animals request was a joke but then realised it was Lady Gaga. Simon is an animal-lover and wasn't against having the lambs running around, but he said no because of health and safety."
The eccentric singer also recently had a request to have lions accompany her to the MTV Video Music Awards turned down.
The source added to Britain's Daily Mirror newspaper: "After the MTV Awards she knew that getting animals on stage was a long shot but she was just pushing her luck.
"However, she had other ideas and is thrilled with what the 'X Factor' team has devised. People are still going to be stunned."
British health and safety officers also cracked down on singer Mariah Carey's diva demands last month when she appeared to turn on a shopping center's Christmas lights in London.
Carey requested 20 white kittens and 100 white doves to accompany her at the extravagant switch-on ceremony at the Westfield shopping center, but health and safety officials denied her wishes — because animals are not allowed inside the complex.
The singer did, however, arrive in a Rolls-Royce and was accompanied by 80 security guards as well as a 15-strong entourage.