Yeah, I tried this a few times back when I had a DS.
Assuming you're not using an emulator (I don't know how it works there), you need some kind of flashcart for the DS, preferably one that supports automatic DLDI patching (virtually all of them have for a long time). I'm not sure what's on offer these days - I know there's ones that are even compatible with the DSi and 3DS; back when I had a DS the big brands were CycloDS, AceKard and R4 (among several others), it's my understanding that R4 have stopped producing though some counterfeits of it are floating around.
Beyond that, it's a matter of simply following the setup as the Lemmings DS readme suggests. I think it's more or less comparable in difficulty to setting up the Lemmix editor, maybe a bit simpler even. I remember not thinking very highly of the level editor for it, though; but fortunately it also had a convertor to convert LVL files to its format.
The website of the project is here:
http://www.mrdictionary.net/lemmings/(Yes, the same guys who made the Objection generator. xD)
