"It is time now for Mr Armstrong to face the consequences of his actions. This includes returning all of the funds paid to him by SCA, which totals more than $12 million," the lawsuit said.
"Mr Armstrong has no legal right to retain any prize money paid to him by SCA because he is not the official winner of any Tour de France titles."
The 35-page state court filing in Dallas would deliver a financial blow as well as put Armstrong under oath about the doping scandal that ruined his cancer-comeback story and tainted his Livestrong Foundation charity work.
"Lance Armstrong perpetuated what may well be the most outrageous, cold-hearted and elaborate lie in the history of sports," the lawsuit said.
Armstrong was banned for life when the US Anti-Doping Agency found overwhelming evidence that he was at the heart of a sophisticated doping scheme when his US Postal Service team dominated the Tour de France.