How would that work? Same rules as the multiplayer mode (anyone can control any lemming, everyone works from a shared pool of skills)?
Co-op is clear, as you described.
Competitive: you each have your own lemmings: blue-green vs. green-blue. You have your own start point and end point on the same map. You can only control your own lemmings. Your goal-point will accept any lemming. Hilarious chaos ensues.