If you're going to have a lawn, make it red creeping thyme.
It barely needs water after the first year. It tops out around 2 to 3 inches and never needs mowing. It produces a carpet of magenta flowers in summer that bees and butterflies cover like a feeding station.
It smells like thyme when you walk on it, because it is thyme. It's the same genus as the culinary kind, and edible.
Deer won't eat it. Rabbits won't eat it. Grass is crowded out by it.
It's hardy in most of the US (zones 4 through 9), tolerates poor soil, and handles moderate foot traffic.
Honest caveat: creeping thyme isn't native to North America. But neither is your lawn.
Kentucky bluegrass is European. Bermuda grass is African. Every square foot of creeping thyme replacing turfgrass is net positive for pollinators, soil, and water use.
If you want a fully native ground cover, look into Pennsylvania sedge for shade, pussytoes or wild strawberry for sun, and moss phlox for rocky spots.
But if you're going to have a lawn, make it one that does something.