Rapoport had reported that Lockhart "says the NFL will file a appeal to stay the ruling in the court of appeals, as well as request for expedited action" in the Elliott case.
As Mike Garafolo of NFL.com noted, that essentially means the NFL is hoping to make Elliott serve his suspension this season after a Texas District Court awarded Elliott an injunction that prevented him from having to serve any suspension during his lawsuit against the league.
As for the Commissioner's Exempt List, being placed on it would have meant Elliott could not attend practices or games but would have been allowed at the team facilities for various non-football activities such as attending meetings or getting treatment. He would be paid his full salary and receive benefits, however.
The NFL Player Personnel Policy Manual describes the Commissioner's Exempt List thusly:
"The Exempt List is a special player status available to clubs only in unusual circumstances. The List includes those players who have been declared by the Commissioner to be temporarily exempt from counting within the Active List limit. Only the Commissioner has the authority to place a player on the Exempt List; clubs have no such authority, and no exemption, regardless of circumstances, is automatic. The Commissioner also has the authority to determine in advance whether a player's time on the Exempt List will be finite or will continue until the Commissioner deems the exemption should be lifted and the player returned to the Active List."
Roger Goodell most famously used the Commissioner's Exempt List on then-Minnesota Vikings running back Adrian Peterson in 2014 during his trial for child abuse.