The lawsuit was filed by Armstrong's former U.S. Postal Service teammate Floyd Landis. The federal government joined in 2013 after Armstrong publicly admitted he cheated to win the Tour de France seven times from 1999-2005.
Armstrong was stripped of those titles and banned from competition.
Armstrong has also taken huge hits financially, losing all his major sponsors and being forced to pay more than USD 10 million in damages and settlements in a series of lawsuits.
Armstrong's legal team didn't immediately respond to requests for comment.
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Landis, himself a former doping cheat who was stripped of his 2006 Tour de France title, sued Armstrong under the federal False Claims Act, alleging Armstrong and his team committed fraud against the government when they cheated while riding under the Postal Service banner.
According to court records, the contract paid the team, which was operated by Tailwind Sports Corp., about USD 32 million from 2000 to 2004. Armstrong got nearly USD 13.5 million.
Landis stands to receive up to 25 percent of any damages awarded.
Armstrong claims he and the team don't owe the Postal Service anything because the agency made far more off the sponsorship than it paid. Armstrong's lawyers have introduced internal studies for the agency that calculated benefits in media exposure topping USD 100 million.
The government has countered that the negative fallout from the doping scandal tainted the agency because of its association with Armstrong.
"Giving Armstrong 'credit' for the benefits he delivered while using (performance-enhancing drugs) could be viewed as an unjust reward for having successfully concealed his doping for so long," Cooper wrote.
"(But) disregarding any benefits USPS received from the sponsorship could bestow the government with an undeserved windfall. The same could be said of Landis, whose role in this entire affair some would view as less than pure."
Landis attorney Paul D. Scott said he was delighted" to see the case move toward trial.
Armstrong had been one of the most popular sports figures on the planet before his cheating confession.
His personal story of recovering from testicular cancer that had spread to his brain, while forcefully denying persistent rumors of doping, had built his Lance Armstrong Foundation cancer charity into a USD 500 million global brand and turned him into a celebrity.
The foundation, which removed him from its board and renamed itself Livestrong, has struggled in the aftermath as donations and revenue plummeted.