In a court filing Monday, the lawyers said former Deputy Chief of Staff Bridget Kelly is not entitled to the broad exemptions she has asserted as she seeks to quash the subpoena.
"The real problem here is that Ms. Kelly does not believe there is any proper subpoena that can be issued to her," the lawyers wrote.
The legislators want Kelly to turn over emails, text messages and other documents that involve a plot to block traffic near the George Washington Bridge for political retribution against a Democratic mayor who didn't endorse Christie for re-election and whose town experienced the gridlock.
Kelly and Bill Stepien, Christie's two-time campaign manager, have refused. They're asserting their Fifth Amendment rights against self-incrimination in attempting to quash the subpoenas. They say they fear the possibility of criminal prosecution amid an ongoing federal criminal investigation.
Oral arguments are set for Tuesday.
Some 32 other people and organizations close to Christie, including his re-election campaign and the Republican State Committee, have complied with subpoenas or are producing documents to comply.
Christie fired Kelly in January after emails obtained earlier in the investigation showed she set the lane closings in motion with a message: "Time for some traffic problems in Fort Lee.
The response, "got it," came from David Wildstein, another Christie loyalist who worked at the agency that runs the bridge.
While no emails or text messages link Stepien to the planning of the scheme, Christie cut ties with him after emails showed him discussing press coverage of the traffic jams with Wildstein and referring to Fort Lee's mayor as "an idiot."
Christie, who originally said Stepien knew nothing about the scheme, later revoked his recommendation that Stepien become the next state GOP chairman. In distancing himself from a once-trusted adviser, Christie said he was disturbed by the "callous indifference" shown in the emails. In the press conference, Christie apologized repeatedly for his staff's "stupid" behavior while maintaining he knew nothing of the planning or execution of the traffic-blocking plot.
Wildstein, who quit his job at the Port Authority of New York and New Jersey, claimed through his lawyer "evidence exists" that Christie knew of the lane closings while they were happening.