NeoLemmix Official Lemmings Games
Many Lemmings fans will already know about Lemmix. For those of you who don't, Lemmix is a Lemmings clone originally developed by Eric Langedijk (aka EricLang), which aims to perfectly emulate the DOS Lemmings games' mechanics, but with additional fine-control features, Windows compatibility, et cetera.
On the other hand, NeoLemmix abandons this idea of perfectly emulating the DOS mechanics (see Traditional Lemmix if you want that), and instead modernizes and improves the engine. As well as being available for use in new custom levelpacks, NeoLemmix conversions of all official games have been made, as well as a couple of notable historical fangames.
These players don't just blindly slap the official games' levels into an updated engine like many other engines have done; every level has been examined and many have had adjustments made to "NeoLemmix-ise" them. The exception is Copycat Lemmings, as the underlying capabilities of it and NeoLemmix are similar enough that such changes are not nessecary.
You will need the NeoLemmix Engine to play these.