We obviously can't control extended droughts, but we can minimize damage hot, dry periods cause if we act before they occur. The biggest factors why lawns fail during extended dry spells, is that they weren't healthy going into the drought, or the grass type was wrong for the area it's growing.
First, do everything you can to make your lawn as healthy as possible while conditions are good for growing lawns. Here are the basics for a healthy, drought-resistant lawn:
Regular fertilization that develops strong root systems enables your lawn to better survive the dry days. Don't over-fertilize or use a fertilizer that encourages more top-growth (which means more mowing).
Keep water-hungry weeds out of the lawn.
Aerating your yard regularly helps a lawn develop stronger root systems, and reduces thatch buildup. If you have a thatch problem, aerate twice a year for several years (once in the spring and again in the fall). If aerating in the spring, do so before applying a pre-emergence herbicide, typically used to control crabgrass and other grassy-type weeds. Thatch buildup reduces the amount of water penetrating the soil and encourages shallow root development.
Increase your mowing height as temperatures increase. This will conserve soil moisture and strengthen root development.
Remember, just as lawns turn brown from extreme water shortages, they will also return to their natural thick green state when conditions improve, usually in the fall— just don't panic.
Select grasses that will work in your climate
Next, make sure the grass you're trying to grow is designed for the area. Don't try to plant a Kentucky Bluegrass in the deep south. You're only asking for expensive problems. If you live in the southwest, re-think the entire idea of having a lawn. Green lawn expanses were never intended to be grown in the desert.
Just about every turf grass requires regular (weekly) watering and if you live in an area prone to extended hot, dry spells with regular watering restrictions, a lawn may not be in your best interest. There are a multitude of other options available (see xeriscaping or even a synthetic lawn maybe the right choice).