Not very many write-ups on this, but RantSports had one (LINK).
This story and many tweets do stress that, at the moment, there is no evidence to support the claim, but I would think that, in a scenario where it was true (lots of people on Twitter going out of their way to point out the lack of evidence at the moment) the timing couldn't be worse as you would have to make a bumbling transition to one of the coordinators more than likely with no time to hire someone impactful. There would also be considerable difficulty getting top-tier recruits to come to LSU, I would imagine. Les leaving because he doesn't want to coach anymore is something they could likely manage fairly smoothly, but in any other case, I would see LSU as desperately unprepared.
EDIT: PatWhiteSports is now tweeting that they have a source claiming that this rumor is not true.