Probably because NeoLemmix does a lot of checks that normal Lemmix doesn't, thus, it needs more power to run. In fact, Lemmix (in traditional form) can exhibit those kind of behaviours too, under intense circumstances (such as levels with very high numbers of lemmings); it just takes less to push NeoLemmix to that point because it does more work.
This is especially true of blockers - under traditional mechanics, the trigger area grid is made up of 4x4 sections, whereas in NeoLemmix, it's pixel-perfect. This essentially means that the engine has to do 16 times as much work each time a blocker is placed or removed, since what was previously one spot of the trigger map is now 16 spots. In practice, it isn't *quite* 16 times, because the blocker's fields don't cover quite as large an area as they did before, but it's still a LOT more. Likewise, any skill that applies a terrain destruction mask can no longer just blindly slap the mask down, but also has to check if any of the pixels shouldn't be removed (due to being steel or wrong one ways). Likewise, climbers now perform terrain checks more often (though the checks themself aren't any more intensive, I don't think; they're just more frequent), builders perform a couple of extra checks each step, etc.
That being said, on my system - a laptop from about 3 years ago, that was probably somewhere between "good" and "great" for its time but definitely nowhere near top-of-the-line - it doesn't have any problem with fast forward or time skip; it does sometimes take a while to load a saved position, depending on various factors (how complex the level is, how many lemmings, what skills are used). Maybe try running it on a different system, or with less processes running in the background? I might see if I can get an older PC up and running to see just how bad the performance issues are and if I can identify anything that's really straining and if there's any way to improve it. Indeed, some of the earliest fixes I implemented could probably be implemented in more efficient ways; the hard part is tracking down exactly which ones cause the big issues when my system isn't one where the issues are particularly noticable. But, I would certianly rather not make it unusable on older systems if I can avoid it.