Turf grasses are tough old things and so long as you have healthy and desirable turf grasses in your lawns then they should be capable of coping with the extremes of drought.
If you have a newly renovated lawn with seed or turf, then the investment needs protecting and the lawn watering daily or every other day to aid establishment of the new lawn but do not let the water run off the area you are watering. Little and often.
Sometimes, brown lawns are cool and even automatic irrigated lawns will not keep up with a prolonged dry spell. Wetting Agents help get any available water get down into the root zone where the turf grasses can really benefit from it and deeper rooting is encouraged by doing this.
Remember that the natural evapotranspiration water loss per hour could be 4mm per hour when temperatures are 25 degrees centigrade and higher when temperatures increase. This means that you need to replace 4mm of water volume per hour with artificial irrigation or rainfall to replenish this naturally occurring water loss through the sunshine beating down on the lawn surface. It is therefore really easy to get into a water deficit in no time at all during a sunny week with minimal rainfall.