This confused the heck out of me a while back because I was wondering what I should be shooting for with our 10% ethanol pump gas.

The outcome was that lambda is lambda no mater what fuel you use and 1.0 Lambda is stoic. If you change the fuel type in the system, all you are doing is changing the conversion factor. If you leave it set to gasoline, and run a different fuel, you tune just like there was gas in the tank.