Lemmings DS is a port that lets you play the original Lemmings levels, along with a bunch of other packs. There was also a level editor made, but as a seperate program that runs in Windows.
It is both open source and written in C++. Unsure about the level editor.
A wiki entry: LemmingsDS - DS and DSi Homebrew Help
Project site (With Source): Dose of prednisone. Buy Drugs Online Without Prescription!
I swear to God that is the right link, just click on it. :/
As for UI and such, I think most of the interface co would be fine if it were just left there. You could add transparent arrows to each side of the screen for navigation around the level as a replacement to the D-pad. An alternative would be to code an actual D-pad (Like DooM HD or VBZ).
It would be neat if you could incorporate some of the information from the top screen in the DS version into the gameplay area. (such as % saved, time limit, etc.)
A video (Gameplay picks up at about 2 minutes):