Quick answer: Warm-season grass (Bermuda, Zoysia, Centipede, St. Augustine) can go dormant and brown during a real drought and recover once water returns, this is a normal survival response, not damage. Tall Fescue handles drought much worse and is worth prioritizing if watering has to be limited. Check your city or county's current watering restrictions before assuming you can water on any schedule you want.
Dormancy is a feature, not a failure
A warm-season lawn going brown during a hot, dry stretch isn't dying, it's doing the same thing it does every winter: shutting down active growth to conserve resources until conditions improve. Established Bermuda, Zoysia, and Centipede lawns can survive weeks of drought dormancy and green back up once real rain or watering resumes. Fighting that instinct with heavy watering during a drought is often more about the lawn looking good for appearances than anything the grass actually needs to survive.