A tree can be a lawn's best friend, or not.
Most people with home lawns also have trees and shrubs in the landscape. Sometimes trees and lawns get along well together and sometimes they don't.
The shade produced by trees can present some problems for grass growth, as can shallow roots and the dry conditions beneath the trees. Conifers present the biggest problems.
Normal light intensity favors photosynthesis and adequate carbohydrate reserves. As light intensity decreases, photosynthesis decreases as well, and the plant uses carbohydrate reserves from the roots. The grass becomes more succulent and vegetative and its food reserves are drained so much that they can no longer fend off disease and insect attack.
What about shady/moist???
Different grass species have different shade tolerances. Red fescues tolerate shade fairly well, but Kentucky bluegrass does not. These species make up the bulk of lawns in our area.
Competition for water and nutrients from the tree roots will also make the area beneath them inhospitable for grass growth. Again, red fescue will tolerate this condition better than Kentucky bluegrass. If you plant a blend of red fescue and Kentucky bluegrass for your lawn, the species will segregate themselves over the years according to their own habitat preferences until you'll find only the red fescues beneath the trees.
And that's not all the trees. Conifers like spruce and hemlock produce such dense shade, dry conditions, and a thick bed of needles that not even the fescues will tolerate them. You may actually be thankful that there is no lawn grass that will grow under these conditions. If there were, you'd . . . have to mow it!