How long can whiptail lizard go without any water?

This is not a question with a concrete answer, because it depends on a LOT of factors. Desert species tend to get most of their moisture from the food they eat. If they don't have food available, they will dehydrate a lot faster. In addition, it depends on whether they have a cooler, humid place to retreat to (such as a burrow), as high heat and dryness will cause them to dehydrate faster.