It is impossible to KNOW. However, based on statements made and actions taken, it is possible to infer what the parties are thinking.
which also means it's possible to infer that LSU has some reason to believe they have a "for cause" case.
For BK to sue LSU, he seems to believe he was not fired for cause, based on what Woodward told him and public statements in the next 3 days. Therefore, LSU owes him the money. He might choose to settle for a lump sum up front if it is attractive enough, and reduce it by some amount if he wishes to get out from under the mitigation clause, but LSU does not have the right to tell BK he is fired for performance, then change their mind and tell him after the fact that it was for cause.
see here is where what we don't know plays a huge part in this whole story.
we have no clue what was said behind closed doors between LSU and Kelly.
the only thing we 100% know is that Kelly was open to negotiating (email that was obtained through FOIA confirms this).
literally everything else is from sources and not all tell the exact same story.
LSU may very well have told Kelly (something along the lines of) "hey, we could pursue this violation of your morality clause, but we don't want this to get ugly, let's negotiate and keep everything quiet and we both go on our way." Kelly and his agent agree.
He then gets fired and public is told it's for performance. Negotiations begin.
Interim President and the AD he was negotiating with both get replaced.
New people in charge of negotiating and things turn sour.
Probably at least in part due to the hit jobs the media has run on Kelly since he left.
BK goes on the offensive, slaps LSU with a lawsuit and wins Round 1 of the PR battle.
If LSU claims the termination was for cause, they have totally blown it by not following the terms of their contract:
oh LSU has fucked this whole thing up from the very beginning.
I said that even before all this shit popped up.
this is a masterclass on how NOT to fire a guy.