Actually, I can see him accepting. In the spirit of the original Roman Title, to deal with a crisis and for a fixed duration (1 year renewable). And then follow the exemple of Cincinnatus and leave power to institutions he helped put in place.
No that's not the type of person Lafayette is. When he was leader of the National Guard he held so much power he could have destroyed the radicals, he could have overthrown the assembly, and we all know he could have overthrown Louis put the Dauphin on and ruled as regent. Had he done the first one he wouldn't have slowly been outmaneuvered. Had he done the last one he could of moderated and secured the way for the constitutional monarchy.
But now that I think about it, you could have the POD be a personality change in prison. Perphaps his wife and children aren't able to visit (saves their lives) and that cause Lafayette to break. So all he can think is I had the power I should have used it, dam Louis for running, etc. Then when he gets offered he accepts and builds a new France. Basically his ideals are the same, but he realized that to get there he has to work harder.
Also with his OTL personality how would he not decline in favor of a constitutional monarchy, which was what he believed was best for France?