What Lane is doing is not wrong at all. He wants to upgrade jobs and be at LSU. It isn't his fault that the football calendar is set the way it is.
If anything, he is trying to do right by the players and stay and coach amidst the fanbase hating him. If he just goes to LSU immediately, and doesn't coach Ole Miss, Ole Miss will be less likely to have success in the playoffs.
Ole Miss administration is just trying to spin the narrative becuase they were unable to keep Lane, the best coach they have ever had, and have to save their a** when Ole Miss turns back to being a mediocre program.