[StoryProgression] itself should produce a consistent stutter every time it performs a large calculation, which normally only occur every 10 sim-minutes or so.
A number of users have noted the mod is simply slow in general, and not the "lag every 10 sim-minutes" effect I would expect.
Leads me to believe the mod is coming into conflict with other CC installed on the user's setup in some undefined manner.
Personally, I keep my setup reasonably clear of custom content, I only have a couple of downloaded hairs installed. The remainder is all EA Store content.
That difference may explain why I have not been able to reproduce the lag issue.