This was in retrieving prize money from insurance company SCA Promotions.
A Texas judge on Wednesday rejected Armstrong's request to prevent an arbitration panel from reviewing the bonuses he was paid before admitting to doping throughout his fabled career.
He was banned for life and stripped of all results dating back to August 1, 1998 - including seven successive Tour de France titles - for doping, something he belatedly confessed to in an interview with Oprah Winfrey in January 2013.
Dallas-based SCA Promotions is seeking the return of 12million US dollars - Tour de France prize money of 1.5million US dollars in 2002, 3million US dollars in 2003 and 5million US dollars in 2004, plus 2.5m in costs paid in 2004 - plus interest, costs and damages.
Jeff Tillotson, an attorney for SCA Promotions, told Press Association Sport: "It is beyond dispute that he perjured himself in our (2006) proceeding. The only thing left to resolve in this is in what manner should he be punished.
"He should not be allowed to retain the benefits he got from lying. He used his lies to obtain more than 10million dollars from us.
"In addition we had several million dollars in legal fees and suffered an enormous amount of damaging publicity. Those are factors we're going to ask the panel to consider."
The panel will meet on March 17 to discuss the case, which is a civil proceeding as the statute of limitations means he avoids criminal charges.
"Whether he faces criminal or not, he did benefit financially tremendously from his lies," Tillotson added.
"I think everyone would agree that someone who lies to get millions of dollars ought not to keep that.
"That's what we will be asking the arbitration panel to do."
It is one of two major cases Armstrong is subject of.
The penalty in the second is potentially even greater as the Texan is accused of defrauding the United States government over its sponsorship of the United States Postal Service team which Armstrong headed.
It could cost Armstrong 120million US dollars, three times the sponsorship value, but there is plenty of time to run as the case is at the procedural stages.
Armstrong's long-time lawyer Tim Herman was not immediately available for comment.