File extraction for Mac is tricky because they have this screwy (fine, "special") concept of multiple "forks" within a file. Basically (this is a bit of a simplification) the Mac think of a file as capable of having multiple streams ("forks") of data, rather than just one single stream of bytes. In particular, many of the Mac Lemmings game files store the majority of "interesting things" (eg. graphics, sound, etc.) in the resource forks of the files.
If your extraction program doesn't have an option to extract all forks, you can end up with just the data forks of the files, which for many Mac Lemmings game files is empty (ie. everything of interest stored in the resource fork instead). This is done probably because there is a predefined structure to data in the resource fork of a Mac file.
Anyway, I would still think that StuffIt should be Mac-aware enough to have an option for you to extract both data and resource forks, but even after doing that it will probably take you a separate program to parse the resource forks extracted.
I have actually done a bunch of that programming work a long time ago with the help of documentation scrounged from the web and from a colleague that still has really old Mac programming books. And as earlier parts of this thread attested, I did the extraction work on the Apple level, so I guess I can pass that onto you. But be disappointed--because it is a special graphics file, the level file itself will not contain any terrain, it will just have the entrance and exit. The terrain is all in the graphics.