Such a test will give your soil's pH, organic matter content and nutrients needed to balance it. Organic matter increases nutrient-holding capacity and improves aeration and water retention. Thatch chokes out grass plants, prevents air, water and nutrients from reaching the soil, and promotes almost every possible lawn problem. Aeration and a brisk raking should remove much of the thatch. This encourages deeper rooting and allows water, nutrients and organic matter to feed the soil.
Earthworms are terrific aerators.
Lots of worm holes in the lawn mean the job is being done for you. If your soil test results show the need, add organic fertilizers. They improve the soil's ability to retain and release nutrients and they are alive with beneficial micro-organisms which speed up decomposition of clippings and thatch. Keep the mower blades sharp so you don't damage the grass. Taller grass will crowd out weeds, grow longer roots and shade the soil.