If you use DOSBox emulator (or possibly even just real DOS, as it might be due to the modern hardware configuration of your PC) to play the copy of Lemmings 2 you have on your CD, you might run into an issue where the game would mostly run okay, but doesn't let you load or save your progress (ie. the "Load" and "Save" buttons on the main screen don't work at all). There's a fix for that which I attached here. You save the file and put it in the same folder where the game's EXE file (L2.exe) is located on your computer, and in DOSBox you run this L2-FIX program instead of L2 itself.
This fix comes from abandonia.com's version of Lemmings 2. I was going to direct you to that site so you can download from there instead of the attachment here, although I decided not to as that site has a bit too many ads that try to resemble download links to bait you into downloading their crap instead. (The abandonia.com site itself is fine other than those ads, and these sorts of ads are sadly not uncommon amongst websites that are ad-supported.)