Jeff Tillotson, an attorney for SCA Promotions, said something had to be done when a party in the case "lied at every step of the way." The language of the settlement allowed the panel to handle any future claims about that settlement, he argued.
"You tried to hurt us - legally, (in) public relations," Tillotson said. "What's the penalty for that?"
Tillotson also said Armstrong's attorneys had previously tried to get the panel to issue sanctions after the settlement against his side.
Armstrong's attorneys say state law protects their client in such cases. Even if Armstrong lied under oath, that would not be enough to reopen the case, said Tim Herman, Armstrong's longtime attorney.
"There is no case ... that gave an arbitration panel any authority beyond the conduct of the proceeding that was going on before them," Herman said.
Parker said she would issue a ruling soon, likely early next week.