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[The Fifth Horseman]

Lemmings (Original)
From Abandonia
Problem: No Music, Slow

Oh No More Lemmings
From DosGamesOnline
Problem: No Music

Lemmings Xmas Package
From Abandonia
Problem No Music

Lemmings 2 Tribes
From ???
Problem: Keyboard controls only
(it is a Sega port, all the Windows ports I could find were either demos or not working)

Dammit kid, read the stickies in Troubleshooting.
You need DOSBox to run DOS games properly in Windows. Otherwise you get (surprise, surprise) no sound, extremely slow gameplay and quite possibly crashes.

All New World of Lemmings
From: Dosgamesonline
File Format: A01,A02,Ao3,Ao4,AO5,ARJ (What program do I need to run them?

ARJ is an archive format, similar to ZIP.
A01 through A05 are parts of a multi-volume archive (pretty popular back when floppy disks were the primary means of transferring files between PCs).
So, you don't run it... you unpack it first. Like, with WinRAR.