Q.problem with feeder roots
Please advise us on problems on growing shadier grass in our lawn, around 600 square feet and facing difficulty with the feeder roots damaging the green grass for growing. Some facts at the site:
(1) The aged trees around the site
(2) It’s a hill and rocky area below the 5 feet of the subject lawn area
(3) We have sufficient water

Here are some links for you.
You may want to consider a ground cover instead of grass. This could be more successful and more consistent in the long run.
https://www.gardeningknowhow.com/lawn-care/lgen/growing-grass-shade.htm
https://www.gardeningknowhow.com/lawn-care/lgen/shade-tolerant-grass.htm
https://www.gardeningknowhow.com/ornamental/groundcover/gcgen/ground-covers-under-trees.htm