I was just talking to a local Landscaper and he said that seed for Lawn that take less water are all invasive varieties that many states don't encourage. I sure wouldn't want to plant grasses like that. Yes they might not need as much water but when they take over whole states and everyone is putting poison on their lawns to try and get rid of them and they don't work, all it does is pollute our water sources. That doesn't seem like a very good way of being good stewards of the Earth to me. Don't mean to be polictial but it is a real concern for me.
I'm definitely not a lawn expert, but I doubt that all low water lawns are invasive and the ones that are, are probably only a problem in certain areas. The trouble is some things that get by on less water will grow much more aggressively if they get more water than what they need to survive, so if you take a grass that would be a nice low-water lawn in the West where we don't get as much rain and move it to the midwest or the south where the natural rainfall is much higher, maybe it could be invasive, but in a drier climate it'll behave fine as long as you don't give it more water than it needs. And if you can do your lawn with grasses that are native to your area then you definitely shouldn't run into problems with invasiveness.