Brad Edwards just on ESPN, laid out scenarios.
Arkansas beats LSU - LSU probably still plays in SEC Championship vs. Georgia (Top 2 Teams in BCS rakings in SEC, then use head to head record to determine who plays in SEC Championship) He thinks Arkansas stays at 3 even if they beat LSU. This is assuming Alabama beats Auburn.
If LSU beats Arkansas, then LSU loses to Georgia in SEC Championship - Georgia wins SEC, plays in Sugar Bowl, and LSU still plays Alabama in National Championship as long as Alabama beats Auburn. This is crazy since neither team wins their Conference Championship game.
IF LSU wins 1 out of the 2, then they will be in National Championship assuming Alabama beats Auburn. If Alabama loses, LSU may not need to win another game and still could be in it.
Only way Arkansas can get to Championship is to win out and have Alabama lose to Auburn or have LSU lose to Georgia.