It's not like the saints can just chose to select all LSU players and haven't done so.
For the saints to select a LSU player he needs to be the best player available at their pick in their opinion. Sometimes, they can be even be searching for a specific position, so even if there is an LSU players as the best available it might be of a position they just don't want, maybe they even drafted another player of the same position earlier in the draft and don't want to double down.
So, before thinking the saints have something about drafting LSU player people should show situations where an LSU player was absolutely the best choice and the saints just ignored him.