someplace on one of these forums, there is a link to a place that sells several different mixes of seed to plant that should eliminate inputs. if i recall, it was a mix for washington state, so you may need to put your own together. there were 3+ plants in the mix.
something like white clover + a rye grass (or winter grass) + a
perennial grass like St Augustine should serve you well there. I have done absolutely nothing to my lawn other than transplant some St Augustine. I have patches in the shade where drought allowed the
trees to suck the moisture out too much, but some
wood chips and charcoal might have helped that.
My yard is mostly St Augustine, creeping charley, white clover (low growing), dandelion, another nitrogen fixing weed in the harder compacted parts of the yard, a bit of nut grass and a few random annual grass and weeds. The part of the yard that has been driven on a bunch has turned into a compacted weedy mess of mostly wire grass, but other than that, it is pretty good 8 years, no
water, fertilizer, weed control, seeding, etc.
Considering planting a self seeding annual grass to try and cut down on the non-nitrogen fixing weeds in the yard. One key to some grass is to cut it high and thatch it only when it needs it.
.... did a few searches to find the link for you.
http://www.protimelawnseed.com/products/fleur-de-lawn found in this
thread:
https://permies.com/bb/index.php?topic=4418.0 after searching the forums with this search term: lawn "seed mix"
that search turns up some other good threads on the forums that may help you in your efforts.
hope something helps you in your journey.