The current document (via The Verge) says that using non-governmental email systems violates the Presidential Records Act of 2014, which requires the use of "official federal government email to conduct government business." The Lawyers' Committee must be able to search and log any emails used by advisory members to prepare its case. According to the filing, Commissioners promised to search their own emails and identify those that "they believe are relevant, and then forward those emails to Defendants' counsel." Wait, what?
It's hard not to think of the endless tirades against candidate Hillary Clinton's use of a private email server during the last election, of course. A federal judge ordered the release of Clinton's emails from her tenure as Secretary of State, the FBI investigated her emails (twice) and then said it would not press charges, after all.
The advisory committee, for its part, states in the filing that the "defendants do not, moreover, recall making any definitive statements as to email addresses being used by non-federal commissioners," and that the specific email accounts are not relevant.