The defensive end and cornerback on that side tackle the running back to that side whether the QB gives him the ball or not. The same holds true for the DE and cornerback on the other side. The two inside linebackers are responsible for any runs up the middle. The two safeties roll to the side of the fake or handoff to stop a throw in the flat or to that side.
I think that will stop the spread offense in its tracks. Everybody on the defense has an assignment. Play your position and make the plays. Period. LSU has the athletes to execute it and make it happen on defense.