PC versions of Lemmings are an entire topic of their own.
But basically it comes down to this.. I don't know if there is a windows port of any lemmings game available, so keeping that in mind I'll talk about the older stuff.
Lemmings was released for the DOS operating system, like a lot of games back in the early 90's. However getting DOS games to run in windows is notoriously difficult unless you luck out with a particular game.
It's not use trying to go into the technical details, but it is worth stating that on modern systems like XP and Vista, DOS games are a lost cause.
You need to get a DOS emulator, the most popular is DOSBox. It has a sourceforge page and it's own page (they may be shared I dunno) where things are updated and kept track of.
Basically what DOSBox does is emulate an entire 286/386/486 machine depending on what you need. The keyboard, video, sound, etc all respond like hardware from the DOS days so if you already remember how to use DOS it's not much different. Although you do have to become familiar with setting things up and ideas such as mounting disks, etc.. There are a LOT of front ends out there that help automate the process and set up a default profile for you, so you can just boot up DOSBox and you arrive at a C prompt with a virtual hard drive all ready to go with whatever you may have installed on it from the last session. Virtual drives are just directories on one of your normal drive that the program uses as a base directory to mimic a drive structure. Even better some front-ends allow you to make profiles for every individual game or program you want to run, if its already installed you can just link to its directory and executable file, or you can even run the profile in setup more, where it does its best to start DOSBox with the profile specifications you input (what resolution, refresh, soundblaster, etc) and runs the setup program so you can install it on your DOSBox drive/directory.
So in dosbox you might have a C:\ drive and have windows installed and some games. In Windows XP/Vista explorer it will look like any other file/directory structure and won't interfere with your actual windows install either. so your drive might be on your D:\ drive on your PC and it would look like
D:\dosdrive\
d:\dosdrive\windows
D:\dosdrive\games\doom
etc, in your windows file explorer. that all probably sounds confusing, but you'll understand once you use it. You can also mount CD rom drives so you have CD-ROM access in dos, and you can either use a Daemon-Tools or other CD utiliies virtual drive to mount a disc image of an old game, or use your physical drive and stick an old games CD-ROM in it, having access.
http://www.dosbox.com/
It's really easy to learn and understand, so don't be frightened.. Although it is NOT perfect they work hard on it and make updates all the time, and a large majority of dos games run just fine, even some 3D games like DOOM or Descent, etc. Lemmings should surely run if you have a copy of a DOS version