LSU has a lot of uncertainty before it, and it's hard to make a bowl projection for the Tigers. It might be hard even after this week's game against Arkansas.
If LSU beats Arkansas this week, and all the teams ahead of it in the BCS rankings win out, the Tigers will almost assuredly head to the Sugar Bowl. If LSU wins out, Auburn beats Alabama, and South Carolina wins the SEC Championship Game, LSU might be looking at the Capital One Bowl. If LSU wins out and Auburn loses its next two games, the Tigers might be headed to the Cotton Bowl; of course, the Tigers could also end up in a BCS bowl game that isn't the Sugar Bowl in that instance, should a BCS bowl game decide to take the Bayou Bengals over Cam Newton's electrifying Tigers of the Plains.
And then there are the possibilities that go along with the Tigers losing to Arkansas.
If they do lose, LSU is likely fifth in the SEC pecking order, behind Auburn, Alabama, South Carolina, and Arkansas. That could mean that the Tigers end up anywhere from the Capital One Bowl to the Outback or Chick-fil-A Bowls. If South Carolina should win the SEC Championship Game, bet on the Tigers heading to Atlanta for the Chick-fil-A Bowl, as the Gamecocks head to the Sugar Bowl, the winner of Auburn/Alabama heads to a BCS bowl game (the loser likely goes to the Capital One Bowl), and Arkansas, by virtue of its proximity to Texas, heads to the Cotton Bowl.
But it's hard to be certain about any of those predictions: there's too much noise in the system. LSU fans are better off waiting for their team to ink a deal before buying plane tickets.