Jay Leno won the battle for Lindsay Lohan because the actress feels "grateful" for the way he's treated her over the years ... sources connected with the actress tell TMZ.
Lohan pre-taped an episode of "The Tonight Show" yesterday ... set to air tonight ... and according to reports, she received a standing ovation when she walked on to the set.
Sources connected to Lohan tell us she has been receiving several offers to appear on talk shows since she was sentenced to jail last week ... but chose Leno because, "He has been nothing but good to her and her family over the years ... and has always been protective of her."
Of course, Lohan was furious with Letterman earlier this year -- when the comic ripped her on his show following a booking fiasco. Video of Lindsay heading to the studio below.
During the interview, Lohan talked about her sentence -- telling Jay she felt "kind of numb" after the judge threw the book at her.
Lohan also talked about the "Gotti" movie -- reconfirming that she WILL be playing the role of John Gotti Jr.'s wife.