Fertilize. Low nitrogen is best. (Using 5-24-20 this year)
I overseed (last week) with 10lbs Linn Rye (perenial) 10lbs Falcon Fescue per 10,000 sq ft.
I also spread pelletized lime. My lawn needs TONS more. Lime is slow to absorb into the soil. I lime spring and fall, at a light rate.
Leaves get mulched "in place". what better fertilizer? Best soils you'll ever run across is "old woods ground".
As summer heat arrives, I start cutting grass longer. In the fall, I return to the shorter hight. (2-1/2")
I don't know how much all this helps (or even HURTS) my lawn. All I know is it needs cutting every 3 or 4 days when it gets water, it looks healthy, and the neighbors keep asking me what I do to make my lawn so green.