The NFL said Fournette violated its unsportsmanlike conduct and unnecessary roughness rules. Lawson was also ejected after the incident in Buffalo's 24-21 win, but no discipline was announced.
Lawson told reporters on Tuesday that he expects to receive a fine, which he will appeal.
Jaguars coach Doug Marrone said Monday that he spoke with Fournette and other players about the fight, which happened late in the third quarter.
Fournette is one of the Jaguars' three offensive captains, and if he does not play, none of them will play against the Colts. Center Brandon Linder is out for the year with a knee injury, and Marrone benched quarterback Blake Bortles in favor of backup Cody Kessler. Marrone said he wasn't considering stripping Fournette of his captaincy because of the fight and punishment.
After Sunday's game, Fournette said he regretted leaving the Jaguars' sideline to get involved in the skirmish.
Fournette's appeal was heard Tuesday by appeals officer James Thrash, a source said.
ESPN's Michael DiRocco contributed to this report.