I don't even have the Windows version of lemmings, but being a Windows 95 program, it would probably store its settings in the system registry. Unfortunately you'll have to figure out on your own where within that vast database of settings (pretty much every Windows program store their settings there, or is supposed to) the lemmings stuff are stored.
Of course, if push comes to shove, you can always export the entire system registry and re-import the whole thing in your other computer. However, it means transferring every single settings for every program and device of your one computer to your other, probably slightly (or very) different computer. So something's likely going to end up broken on the target computer if you try to do that, though perhaps Lemmings would still run.
