I don't know about DiagnoSe, but with Lemmings, put the LemmingsDS folder and lemmingsds_config.txt in the root of the card (you can set them to hidden if you like, it won't effect the game at all, but then you won't have to see them in your list) and you can put the Lemmings DS.nds file anywhere you want on the card. I put mine in my DS Games folder.
As long as you're running the R4's 1.10 firmware, it will auto-patch the game with DLDI and will be ready to go.
I never tried DiagnoSe, so I don't know anything about that one.