This topic might help you get you started:
http://www.lemmingsforums.net/index.php?topic=1618.0NeoLemmix and Lix run out of the box. The Lemmix and NeoLemmix Players allow you to play the original games on modern Windows and they run out of the box.
For custom levels from the level database, Lemmix is recommended, but the setup is a bit more complicated and you need the original DOS versions of Lemmings 1 and ONML for the setup.
If you want to play custom levels without setting up Lemmix there are other options though:
Lix already comes with about 500 custom levels, and on the NeoLemmix website you'll find plenty of level packs for NeoLemmix under the section 'Level Packs'. NeoLemmix allows you use use the original graphics from Lemmings 1, ONML and Lemmings 2, while Lix comes with its own custom graphics.
The only case where you actually need the files from Win95 Lemmings is if you want to run Lemmini or SuperLemmini. If you just want to play the original game, I recommend the LemmixPlayers. Win95 Lemmings isn't all that great...