If your organic soil content was tested low, why not go with composting, or with some sort or rotation of grain-based meals?
Even though there's more labor involved & meals are a little more expensive, in the long run you'll end up saving $$$ not having to mow as much per year because compost / meals don't force anywhere near as much top growth as compared to chemical fertilizers, and thus, your lawn probably won't have to be watered, either!
What you'd need to do to get started is look up local Ag co-op / grain elevators in your area, make friends with the salespeople there, get pricing, make enough space in your garage/shed to stack a few 50# sacks of meal on top of something to keep it dry, and finally, buy a decent commercial-grade spreader with a good agitator system & adequate openings at the bottom.
Examples of some meals, their approx. fertilizer analysis & general rates:
6-2-2 Cottonseed meal...helps acidify alkaline soil, 15-20#/k
.........Corn Gluten meal....pre-emergent rate 20-25#/k
9-0-0 Corn gluten meal....fertilizer rate 10#/k (=1#N/ksf)
2-0-0 Corn meal....acts as turf fungicide too 15-20# k
3-1-3 Alfalfa meal...lots o' micro nutrients too 15-20#/k
6-1-2 Soybean meal...best all purpose meal 15-20#/k
10-6-0 Fish meal.......gardens & beds 5-10#/k
13-2-1 Blood meal....acidifier, best in gardens 5#/k
3-15-0 Bone meal....natural bloom builder 5#/k
1-0-5 *Molasses....micro nutrients + carbs to feed microbes
*Buy ag-grade molasses in liquid form for the best value!
Spray it on the lawn out of a Ortho hose-end sprayer. :waving: