I've been really confused as to why everyone is so fixated on Lyon, and the closing situation more generally.
The problems on the Sox pitching staff are, in order: middle relief, starting pitching, closing. Lyon has been one of the few bright spots, not one of the problems.
Whether he has it in him to be a true, high level, long term closer remains to be seen of course. But in the medium term, Lyon's working out quite well as closer, so they're better off focusing on other areas. And as far as Kim goes, it would seem to make little sense to use him up in the position they're currently having the *least* problems with.