More water is not going to help
Most of our lawns are Kentucky Bluegrass, a cool weather turf. This means that the heat of the summer causes this grass to go into dormancy and turn brown. It is the cooler weather, not more water, that causes this grass to green back up. While we wait for the cooler temperatures to return, keep to the every third day watering schedule and give your lawn a good cycle and soak. It's about getting water deep into the root zone. Leave the grass blades long so they retain moisture and shade the soil, helping prevent evaporation. Try to limit extensive foot traffic too to keep the grass blades undamaged. It is about protecting and nourishing those roots right now.