You had quite major performance problems on your laptop, right? Have you tried the experimental release, and if so - do you notice any lag when saving a state, and if so, how significant? If you could try it, and let me know (a) for an average level, let's say something like Mayhem 5 or 6; and (b) really large levels, for example most of those near the end of Lemmings Plus IV (Insane 18 or 20 is probably ideal - recent releases (all those in NXP form) have all levels unlocked by default).
Number of terrain pieces / steel areas, and actions performed so far, should have little impact (if any). The major factors that are likely to slow it down is the level being large (in terms of dimensions), and lots of lemmings having been spawned (even if some of them have died since). Number of objects will affect it to a lesser degree, but not zero impact. In this regard, Insane 20 is a good level to test, as it has a huge number of objects, 100 lemmings, and is 3 screens wide by 3 screens tall - which I believe is the largest NeoLemmix level currently out there, although I could be wrong.