Grass grew over a dead stump at my house--after it was ground down with a stump grinder.
Be sure to use a good seed mixture (disease resistant and on the A-LIST).
Irrigate--or--water it carefully, every day. Fertilize regularly and never let it dry out.
Not sure about your location, Lovington--however--it is a good time to plant grass seed right now in the northern half of the states. Hurry!
Germination is quick when the soil temp is high--as it is in August.
Weeds are seldom a problem in the fall.
Soil test, topsoil, and starter fert would be helpful.
Use plenty of seed if conditions are not ideal. Double the normal rate is not too much. Look up close and try to get about 20 seeds per square inch.
Remember the germination percent when tested is ideal--but--after that date, the germination declines about 3 percent a month. Much worse if the storage conditions are warm and humid --as compared to cool and dry. Endophytes in the seed add insect resistance--but they are lost if storage conditions are hot and humid.
Heavy shade would be a problem, of course.
Use a shade seed if shady, but it still needs 2 hours of sun per day.
Start 8 weeks before frost.
Only use a seed type suitable to your location and climate. If you have a choice, ask for seed that is resistant to dollarspot, and brown patch.
Expect a few mushrooms from the decaying roots.