In April and May, if water is plentiful, most lawns look great. One of the reasons why they start to look bad in summer is shade. Shade from trees. This is especially true of those lawns with pin oaks or silver maples in them. They produce a thick canopy of leaves, reducing the light penetration to the lawn underneath. What can you do to give the lawn a fighting chance?
First, grow a shade resistant grass species. Zoyisagrass, Buffalograss, most Kentucky bluegrass cultivars, and perennial ryegrass are best grown in full sun. When they don't receive at least 5 or 6 hours of full sunlight, they start to thin out. Instead, use tall fescue, fine fescues (creeping red, chewings, sheep and hard fescues) and shade adapted cultivars of bluegrass such as glade, sydsport, bensun and nuglade.
Second, thin the tree. This is a short term solution, but removal of lower limbs will raise the canopy and allow more light to be received by the lawn underneath. Look up into the crown of the tree as well, and consider removal of crossing limbs or broken/diseased limbs. When removing limbs high in the tree, hire a tree service. No need breaking your leg over a small area of thin turf.
Third, consider bagging the clippings under trees. Bagging removes decomposing clippings, and anything to remove a shading force will help. This process will also remove fallen leaves and sticks from the tree, which can be a smothering influence as well. The whole idea is to help new plants to fill in from additions of seed or from neighboring areas.
Finally, give up. Plant a shady groundcover instead. Lamium, barrenwort, ajuga, bishop's goutweed, lily of the valley, and english ivy are great alternatives. Who says you have to have turf everywhere?