All legit DOS versions of lemmings perform a media check. I know of at least three versions. there maybe more.

1) original 5 1/4 floppy version. The install disk is a key disc. The game will occasionally ask for it when starting, but not all the time. about 8 or nine times it will run without bothering you about the disk, then it will ask again until it finds it.
2) 3 1/2 inch floppy version. this also has the key disk check, but does it EVERY TIME. very inconvenient.
3) DOS CD version. this one also checks media every time i think, but it also wants the CD in the drive to play it's redbook audio. there is a fix mentioned for this one on forums somewhere, as I recall.

I owned the 5 1/4 version, and, like many, quickly found out how to bypass the check, provided you can get it to pass once. after the game has verified the key disk, and exited, you can type

attrib +r russell.dat

to stop it from ever requesting the disk again. this is, naturally, a big boon. It also, naturally helps out with dosbox. Oh No! More Lemmings is protected as well, using the same method (just a different hidden .dat file)

Since I no longer have a working 5 1/4 floppy, it's kinda difficult to install the thing. but for those who do have both the disk and a floppy to use it on...

if you mount your floppy drive in DOSBOX, does the installer run? if so, does the key disk check pass?

If the answers are yes and yes, if you have the 5 1/4 version the workaround listed here works fine. If you have the 3 1/2 version, its' been patched to never create russell.dat, and thus will check every time. In that case, there IS a solution.

On a certain Really old crack site, there's a working DOS lemmings crack, which includes a copy of russell.dat for you. after installing put it in there, and run LEMX.COM, then make russell.dat read only as above. Even though it never creates the file, it will still look for it.

If the installer works, but the keydisk check fails. the crack i'm talking about solves that problem too. if it's okay to discuss it, i'll say where it is.

If the installer fails to work, then you might be able to copy the files from the floppy and use the crack, but i can't test this anymore.

would appreciate it if someone who CAN do this test do it, as I can't anymore.

on 32 bit operating systems i suspect the installer will run just fine, but the jury is out on the key disk. again I can't test. on 64 bit or non windows OS you will have to run the installer under dosbox, and i don't know if that even works.