Much research of late has shown that watering once a week, deeply, is better for all lawns than the practice of a little water every day.
Did the soil test show how much organic matter is in the soil?
Is there a source of compost you can spread on that lawn?
I would spread about 1/4 inch of compost on the lawn and not get too concerned about finding a "fertilizer".

Unfortunately the test results don't show organic matter.

Spreading compost sounds labor intensive. I'd rather spread some organic fertilizer. That just sounds easier. :)

There are organic lawn "fertilizers" available, Ringers, Milorganite and other sewage based materials, and some can get quite expensive. Then there are those that will suggest spreading Alfalfa meal or grains which may help if the soil that turf grass is trying to grow in is somewhat healthy.
Few soil tests do not have something about organic matter although the reference may be kind of hidden. Sometimes that will be reported as Humic Matter, HM, or something else. If the soil test was done by your state universities Cooperative Extension Service ask your county horticultural agent about it.
You might also use these simple soil tests to find out more about the soil that lawn is trying to grow in.
1) Soil test for organic matter. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. For example, a good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drainsâ too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

The report has pH, conductivity, nitrate, phosphorus, potassium, calcium, magnesium, sulfur and sodium.

Thanks for the info! I've looked around a little on the forum and had seen that you had posted the same info in other posts. I was really hoping for someone to give me specific instructions on what kinds of fertilizers I should use based on the recommended fertilizer in my report. I guess there is no quick and easy answer. I should've started this research a while ago but I was slow moving. My first application may just have to be synthetic and that will buy me some time to do more research on organic.

Thanks again!

And one more question. If you spread compost on the lawn, how long does it take to work in? Or how long before the yard doesn't look like it has compost spread on top of it?

It is a bit difficult to be more specific on an on line forum because we cannot always get a good feel for the soil and climate. The questions I ask are meant to help me get your soil in my hands and for you to be my eyes so I can see what I need to.
How long it might take compost to get worked in depends on the soil you have and how active a Soil Food Web is in that soil, and that depends on the amount of organic matter that is in the soil now. The compost will , eventually, develop that Soil Food Web which when active with adequate amounts of organic matter in the soil which will then feed the grass, or other plants, you are trying to grow. But the Soil Food Web needs a food source, organic matter, to be there and work. Little or no organic matter in the soil means a dormant Soil Food Web.

It's hard to find organic fertilizers with NPK that would match up what your soil test indicates you need. Nitrogen gets used up by the grass and also runs off. P and K are more stable in the soil. I would do as recommended and focus on delivering the right amount of N and over time the P and K should come up to.

I would use something like Alfalfa meal which is usually about 2-1-2 or Espoma Plant Tone which is 5-3-3 for a year or two, do another soil test and then reevaluate. After that you'll probably be ok using mainly fertilizers that are higher in nitrogen. The things you'll typically see marketed as organic lawn fertilizers.

Compost is good too but I find that adding fertilizer as well as compost produces better results than just compost alone.

If there's a Starbuck's within your area, go by there for free material. They bag their used coffee grounds for garden use. Spread this over the grass to attract earthworms. They eat the grounds then poop it out. The waste is called "castings," (those small piles of mud-like balls you often see in yards) and is better than anything you can buy.