You should be able to use one single editor for all levels (and the LemmixPlayer with CustLemm support ccexplore talked about, to play all levels, which you appear to be doing already).
I'm not quite certain about your precise setup, but do you have all the vgagrX/groundXo, with X ranging from 0 to 8 (or 9 if you also have the Holiday sets) in the directory pointed to by the CustLemm style definition in LemmixStyles.ini? CustLemm and Original Lemmings are compatible iirc, but you can make a separate folder for CustLemm.
Then use the CustLemm style when editing level, not Orig or ONML. You can exit both Orig and ONML levels with it.
If you want the ONML levels from the original game in the CustLemm lemmix player, you'll have to convert them (change a byte), but for new levels built from scratch, there shouldn't be any issue.
btw, just noticing the initials and your avatar...do you happen to be Hubert and Bart, by any chance?