Ok, I see what's going on now. I didn't realize you're actually using one of the LemmixPlayer programs to do recording and playback, I thought you were using the playtesting feature (F2) of the Lemmix editor.
Unfortunately, as far as I know, there's no way to configure LemmixPlayer so that you both get the correct graphics set and the CustLemm game mechanics. (I should also note that saving the level after changing the style does nothing for the problem; the style is more like a configuration setting for Lemmix, and is not part of the level file. You may have to set it again each time you open the level.)
You have two alternatives:
1) Use Lemmix Editor for recording your solution, using the procedure I mentioned to set the level's style correctly. The disadvantage is that a few handy features like savestates and advance/reverse by seconds, are missing in the Editor's playtest feature.
2) Edit your level to explicitly enforce entrance ordering, by adding duplicate entrances so that there are a total of 4 entrance objects in the level. With 4 entrances, the ordering will be identical in all styles (in ascending order of the entrances' indices). In the case of 2 entrances, this means select the entrance the first lemming comes out from, copy and paste it (which will put a copy in the exact same position), then select the other entrance and copy/paste. The disadvantage of course is that since a level can only have a maximum of 32 objects, the duplicate entrance objects reduce the effective number of objects you can have in the level , though for most levels that shouldn't be an issue.
I should note that even though #2 will solve your entrance ordering problem in LemmixPlayer, there are some minor but notable game mechanics differences between CustLemm and original Lemmings. For example the maximum safe fall distance in CustLemm is 66 pixels rather than 63. While unlikely to affect most levels/solutions, it does mean that in some cases, you may not be able to use LemmixPlayer to record a solution that would've worked in CustLemm.
Ultimately, what we really need is another LemmixPlayer that properly does CustLemm, just like the existing ones for Lemmings, ONML and Xmas.
PS: For me the F11 key displayed the "Inspector", not the "Level properties", which pops up with F10 key. Maybe I'm not using the latest version or something? I downloaded Lemmix from here: http://ericenzwaan.nl/eric/lemmings/lemmix.htm
No, you have the right version, it was just a typo.