So, the traditional "Golf Green Lawn" is a monoculture of one species. Nature does not function with monocultures and this is why plantains, dandelions, clover, butter cups constantly try to grow into lawns. (personally, I see a regular salad bar in most of those plants, but HEY that's just me

Anyway, organic lawn care starts with regular aeration, dethatching if necessary, proper watering, seasonal fertilizing with organic fertilizers (you can use compost and spread it with a fertilizer spreader, diluted liquid fish fertilizer can be applied with one of those (shudder) herbicide sprayers (provided that it hasn't had herbicides and pesticides in it before)
Most important mulch mowing with sharp blades set the correct height.
SO WHAT'S THE CORRECT HEIGHT?
Huh! Yah, the correct height; ask five differnet people, get five different heights. But, here is my take on the correct mowing height. In the summer and spring, mow your lawn to about a four or even a five. This will conserve water as less evaporation will occur.
Now, with mulching or if you don't have a mulching attachment, just not picking up the clippings, thatch can build on your lawn so, it should be raked but, with continued aeration, that should be sufficient.
It is important to keep the soil around pH 6.5 (slightly acidic). On the west coast of Canada (where I and the author of the book live) winter rains acidify the soil, the solution is to apply dolomite lime to the lawn every year which will neutralize acidic pH's and add nutrients such as Calcium and Magnesium.
Aerate the lawn after a wet winter to prevent compaction of the soil. This will give the roots a free draining medium and they will grow much better. It is suggested to leave the core plugs to break down and feed the lawn.
And I will repeat that a regular topdressing with compost. This will help in the decomposition of thatch.
TIPS:
Do not remove grass clippings as they feed soil microbes, which play a vital role in feeding the lawn
To avoid compaction, do not walk on the lawn or cut the lawn after watering or heavy rain
Always cut grass higher than 2 inches.