Cheryl Cole says she signed a VERY lucrative deal to be a judge on "X Factor" back in 2011 ... and even though producers fired her ass before Season 1 ever got off the ground, she wants her money ... more than $2 MILLION ... this according to a new lawsuit obtained by TMZ.
Cole -- a British pop star -- says she signed a "Pay or Play" contract with Blue Orbit Productions that guaranteed her $1.8 million for Season 1 ... and $2 million for Season 2 ... even if she never appeared on the show.
Cole says producers also agreed to pay her a $100k wardrobe allowance for each season, $25k for a stylist, $15k-per-month for lodging in L.A. and $2,500 per month for general living expenses.
As TMZ previously reported, Cole got the chop before Season 1 aired ... because producers believed the American audience wouldn't understand her super-Britishy accent. She was replaced by Nicole Scherzinger ... who was also fired and replaced by Britney Spears.
According to the lawsuit, Cole says producers did pay her the $1.8 mil for Season 1 ... but stiffed her on the $2 mil for season 2, as well as all of the bonus money for expenses.
Cole is demanding more than $2.3 million in damages.
Calls to Blue Orbit have not been returned.