I'm no expert, and this is all on memory from a podcast I listened to over a year ago, but my understanding is that there isn't. There are typically native grasses that do not require water, but are unlikely to stay the green color we associate with a manicured lawn. Any environmental benefits that the grass directly provides is more than offset by the act of mowing it.
I suppose if the vast majority of people used native grasses, didn't water them, and strictly used manual push mowers that there would be benefits, but I don't know if that even qualifies as "lawn"