I couldn't imagine a scenario where LSU would make it, but winning out and making it to the SEC tournament would be making a hard case for LSU. I think it would be possible. I've started seeing some national guys saying that LSU has been playing good ball. I expected our RPI to end up around 80 at the beginning of hte year, but winning out would probably bring our RPI up a pretty good bit. I know Arkansas has some good wins at home which really covers up their poor 1-6 record on road in SEC.
Mizzou on the road would be the game that starts to get LSU recognized. We'd probably want Ole Miss to keep winning if we were looking for NCAA tournament.
Its a really tough thing, because up to this point LSU doesn't deserve to be in the dance. Wins against Auburn and SC at home would have changed my mindset, but at this point I don't think they will let us in, even if we finished super hot.
I don't think we win out (minus SEC Championship), but if we did I'd say about 25% chance. This site says similar: LINK
It has LSU's chances at 23% if they win out minus SEC Champ. SEC wins just don't hold very much weight because everyone thinks the league sucks (good reason to think so).