I googled "green lawn care" and got this:
Organic Lawn Care For the Cheap and Lazy
It seems like very sound advice. Grass is out there competing with other organisms. Make sure conditions in your lawn favor grass and not weeds. The biggest advice he has is set your mower at least 3" high. This will allow grass to grow tall enough to choke out shorter plants like dandelions. Also, you should cut no more than a third of the grass off at a time. So if you're mowing to 3" high, mow by the time the grass is 4.5" high.
Areas where clover outcompetes grass are probably nitrogen deficient. My yard is about 70% clover and other weeds, so I bought 15lbs of 29-3-4 fertilizer with 1% iron. I probaby could have used chicken droppings with similar effect.
Also, grass has deeper roots than most weeds, so if you do water the lawn (which I won't), water deep (1" at a time) and seldom.
I finally scored a used electric lawn mower. The blade was really tearing up the grass, so I gave it a good sharpening. It starts every time, never stalls, is very lightweight, and it has a flip-over handle so you don't have to turn it around at the end of each path. It works for me.
So I'm going to try fertilizer without herbicide, mowing high, and mowing often. Ask me in a few months if it works.