Why does lack of water cause headache?

It's the pressure: Lack of water may lead to dehydration and hypovolemia (decrease in volume of vascular contents). This causes a drop in overall pressure, which can also affect the cerebral spinal fluid (csf). The brain "floats" in a sea of CSF and when the level drops slightly, the brain can be sensitive to those changes. That's one of many reasons!

Dehydration: Dehydraton can serve as a stressor, triggering headaches. Serotonin is released in the face of mild dehydration, ultimately triggering the migraine driver in the brain stem.