I don't think you can say either were "meaningless" at the time they were played...which I suspect was what the OP meant. If that is the definition of "meaningless", then virtually every game except for a SEC championship, playoff or National Champion game was "meaningless".

I consider whether a game was "meaningless" as one where it was know at the time it was played the game wasn't going to have a big impact on the season...not something known through the benefit of hindsight.

Under that definition, LSU hasn't played in a lot "meaningless" games over the last 20+ years. So I guess that would leave, for me, the Florida games in 2020 and 2021.

Going into both games it was already pretty clear LSU wasn't going to have a good season. In 2020 LSU had already been absolutely manhandled in games vs. Auburn and Alabama. They also had embarrassing losses to Miss. St and Missouri. It was the first time in over a decade we were watching LSU just play out the string knowing there was nothing of any significance to be achieved the rest of the way. Commentators were literally laughing at the thought LSU beating No. 6 Florida that night. Then the game was played. LSU surprisingly led at the half. Watching the game via a terrible camera angle because of the fog in the 4th quarter it looked like despite the surprising effort, LSU was going to come up short...until Florida went full Florida and threw a shoe

That allowed Cade York to kick what may be the best FG in LSU history that will ultimately be lost to history because of the game's insignificance. FIFTY-SEVEN yards, in a blanket of fog, dead-center, to win the game!

2021 was almost the same set up going into the game. LSU had just been embarrassed by Kentucky. 11:00 am kick in a relatively lifeless Tiger Stadium. I think, more than anything, I went to the game because it was going to be an absolutely beautiful fall day. 65 F with a bright sunny sky at KO. Zero expectation that LSU was going to compete though. Then they just comically ran all over Florida. LSU ran basically 4 plays in the second half en route to school record.