Planting and maintaining a healthy lawn under shade trees is difficult. Shallow-rooted trees such as maples, pines, and beeches absorb many of the nutrients and much of the water intended for the grass. Trees that cast dense shade block out the sunlight that the grass needs to grow. Grass is especially difficult to grow under pines and other conifers.
Prune some branches from the trees so more light gets to the grass. When seeding shady areas, select shade-tolerant grasses. Seed in the fall, so seedlings have a chance to establish before trees leaf out in the spring. Mow grass in the shade higher than grass in full sun. Water and fertilize more heavily under trees so both the lawn and the tree get enough. Or replace the lawn with a shade-loving groundcover.