LSU averaged about 4 yards per carry (25 carries for 99 yards, NO FUMBLES).
On 2nd and 2 with the lead late in the 4th, why would you do anything but run. I don't care what running play. Anything is better than stopping the clock without advancing the ball. Assuming you aren't going to fumble on that play, there is absolutely no downside to a run and significant potential downsides to a pass. Even on 3rd down, a run still makes sense based on the stats and situation.
Sometimes when you try to be too clever the only one you outsmart is yourself.