45-year-old Armstrong was stripped of his seven Tour de France titles and ban from competing professionally for life in August 2012 after he admitted to using performances enhancing drugs throughout all seven of his Tour victories.
Armstrong's former teammate, Floyd Landis, initially brought the lawsuit in 2010 for fraud.
Landis, himself a former Tour victor caught cheating, would be entitled to up to 25 percent of any money recovered.
WASHINGTON-A federal judge ruled Monday that the federal government's false-claims lawsuit against cyclist Lance Armstrong should proceed to trial, rejecting his arguments that he should win the case now.
The USPS says they paid Armstrong $17 million and spent almost $33 million appearing as the main title sponsor on several of Armstrong's teams.
Armstrong settled a long-running dispute with Dallas-based insurer SCA Promotions for $7.5 million in 2015.
Cooper agreed with evidence that the USPS "received substantial benefits as a direct result of the sponsorship", citing internal USPS communications and valuation studies by third parties.
Armstrong sought to get a summary judgement on the case last April.
1 in 5 Pennsylvania bridges are 'structurally deficient,' report says
According to a construction industry report released on Wednesday, nearly 56,000 US bridges are structurally deficient. With the current $215 million budget, roughly 8% of Indiana's bridges are structurally deficient.
He finally admitted doping in January 2013 during an interview on the Oprah Winfrey show.
A trial date has not yet been set for the case. "The same could be said of Landis, whose role in this entire affair some would view as less than pure".
Armstrong has tried to have the case dropped, claiming that the sponsorship benefited the Postal Service and was worth more to USPS than the $32m it paid to his now disbanded team, Tailwind Sports Corporation.
Lance Armstrong faces the prospect of "financial ruin" after he failed to block a $100m (£80m) lawsuit brought by the U.S. government against him and his former team.
Armstrong's team was already under the Postal Service sponsorship when he won his first Tour de France in 1999.
"As the court's opinion reveals, there is no actual evidence of any quantifiable financial harm to the USPS", said Elliot R. Peters, lead attorney for Armstrong. Landis was stripped of his 2006 Tour de France victory for doping, as well.
"So the government may now proceed to a trial that, as a practical matter, it can not win", he said.