I believe the rule is when a player gets ejected they must sit out the next game. If it happened in the first half they would sit out until the 2nd half of the next game. (1 full game) The NCAA will more than likely suspend him for the season... Remember LaGarrette Blount from Oregon vs. Boise St. When he punched after the game when Boise St was celebrating. He was pretty much being taunted by the Boise St player...but still shouldn't of punched him.
LSU will probably try to self impose a 2 or 3 game suspension to avoid the NCAA suspending him for a season.
I also think that the LSU player may try to appeal any punishment saying he thought the play was still live. He might be able to play after sitting out 1 game while appealing any other punishment. If LSU was smart they would suspend him indefinitely. Just my opinions.