I'm pretty sure Lemmings 2 does have copy protection, and here's the unfortunate reason that I know why:
I first got the game about 14 years or so ago, and it came on two 3.5-inch floppy disks. I installed it on my dad's computer and it worked fine. Unfortunately, a couple of years later, my little sister (who was about 2 years old at the time) got into the disks and pretty much destroyed one of them. The game was still functioning on the computer, but one of the disks was pretty much worthless.
After that happened, I tried making copies of all of the Lemmings 2 files on the hard drive for backup purposes, but the copied .exe file would not work. So now I've still got the game on the hard drive of my dad's old computer (which is now sitting on a desk in my apartment) but I've got no way to back it up in case the computer crashes.
EDIT: After taking another look at my problem, I happened to luck out. Of the two disks I have for Lemmings 2, the one that is destroyed is NOT the one with the .exe file on it. Therefore the original L2.exe file still works fine, and I can make backups of the other files quite easily.