To maintain lush healthy grass under tree shade there are certain methods that need to be followed to have any sign of success. Grass growing under trees is disadvantaged compared to grass growing in full light, as the grass gets less light all year round so it grows more slowly than it would normally do. Because it grows under the protection of the trees themselves, it also does not need to be so rugged, it does not have to be capable of standing the direct heat of the sun, it doesn't have to be tough enough to take the full force of the weather,
and it is also likely to have less moisture as the Tree itself will take up most
of the moisture (i.e. direct rain, full wind force and chill factor and also grass under trees does not suffer from hard frosts). This all adds up to a type of grass that is more likely to die back if mistreated, but the true benefit is a slow growing lawn with delicate soft grass blades that tend to be soft to the touch and a lovely dark green.