Add compost to your lawn. Most cities have free compost available, just check with your parks department. Local stable and alpaca farms may have manure available, it should be thoroughly mixed into your soil or mixed with water to make a liquid compost. BE CAREFUL about store bought compost as sometimes unwanted invasive seeds may be present. Fine Mulch can also be worked into the soil. Check with your local master gardeners or your local botanic gardens for expert advice and guidance.
you could contact your county extension service and get soil sample bags and send it to be analyzed and it will tell you what nutrients you need to make your soil healthy
I would suggest starting with a soil test to see what conditions you are dealing with.
Soil tests are always recommended every few years. Most every speaker in my master gardeners class recommend this for optimal way to address your soil and garden circumstances. The soil test box and instructions can be obtained from your local cooperative extension, unless you want your lawn service to do it.
You have to have a good soil to meet your needs to growing grass or any vegetable gardening. From there you will find out the labs recommendations to promote the growing conditions to include fertilize lime ( pH adjustment) in addition to aerate and seed If grass is desired.
Our turf situation we are found that core aeration is extremely effective to help break up the soil and get better results from seeding. Generally done in the fall aeration and overseeding with top dressing can really improve your turf’s appearance.
Your local Cooperative extension is staffed by volunteer master gardeners waiting to assist you —consider giving them a call (or visit) they may have local information unique to your region to share experiences and possible treatment about your solving your soil situation.
A good general amendment to your garden and turf is a top dressing of organic matter, such as aged compost. This can be spread up to three inches deep on the garden surface and allowed to naturally incorporate into the soil. Amendments should be applied to the entire garden, not to individual plants or planting holes. Beyond organic material, added amendments should be governed by the results of a soil test. Hope this helps!