Hey, welcome back!
Well, generally these days, the method of choice for running the game is Lemmix or Lemmini. Both have been / are being recently updated and improved by new people working from the original code - Tsyu for Lemmini (his version is SuperLemmini) and myself for Lemmix (my version is NeoLemmix). The old version of Lemmix is still also of course available; I even "cloned" CustLemm in it so you can have the convenience of that combined with Windows compatibility and Lemmix features. Editor wise, there's two new ones that I know of - my own NeoLemEdit, which is a Windows-based LemEdit clone that supports NeoLemmix features, and jLevelBuilder, which is more tailored towards Lemmini, as well as the creator's own Lemmings-like game.
There've been a few large new level packs too (as well as the usual small ones here and there) - my own Lemmings Plus II, a sequel to Lemmings Plus DOS Project and as far as I'm aware the first pack using traditional formats/mechanics to have custom graphic sets (with Lemmings Plus III being currently in development, this one being built from the ground up for NeoLemmix); mobius's MobiLems, exit's cLemmings, as well as several compilation packs. There's also Lix, which is a multiplayer-capable fanmade game that's quite popular; unfortunately I can't say much about it myself as it doesn't work on my PC.
I don't know if you heard, but there was also a new official game, called Lemmings Touch. Unfortunately, it's only available on a console that no one actually has <--- slight exaggeration. Playstation Vita.