The defense is improving game by game, but I don't think it's going to matter. The main problem is LSU can't run the ball. With a more "LSU" run game, this team would probably be good for 8-9 wins. As it is, I'm still holding my breath to see if they can get to 7 wins. It was the biggest problem of the UCLA loss, why they couldn't close out MSU strong, and why the McNeese win was still so god-awful.
The reason I don't think it will get better is because it's not just one thing. If you have one thing to work on, sometimes that gets better in a season. The line gets no push, they don't set the edge well, they still get confused sometimes on who's trying to get out on who on run plays, the QB isn't great at knowing when to keep and when to give on the RPO's, and the backs--as a group--have the worst vision I recall seeing in a tiger backfield. I've lost count of the times a back has missed the crease and instead run into a wall on the unusual occasion the line gives him something to work with. That's too many problems to get fixed.
The team has other issues, but that's by far the most important.
For reference on how miserable LSU's run game is, LSU through 4 games, including 2 cupcakes:
2.86 overall average ypc, including 2.33 vs. MSU and 1.92 vs. UCLA. Best average was 3.5 vs. Central Mich. That ain't gonna cut it. LSU has never been this inept in the run game in my lifetime, not even in the dismal 90's. (Actually the run game was not the problem in the 90's.)
You never had to worry about that with Saban or Miles. However fiasco'd the QB situation got--and both had some awful QB years--you could count on them to secure a lead at the end of a game and play keep-away from the high octane offenses enough to combine with defense and usually win. This team has to live and die by the arm and the decision-making of its QB, and he's a year away, assuming his line ever figures out how to keep him upright.