Thanks to Janice for emailing this recommendation:
"In League City, Texas, check out the New York Pizzaria on FM 646. They have two specialty pizzas on their menu that are dairy free. I've tried the Paisano. Excellent!!!"
As it turns out, this is a chain in Texas, so they have multiple locations. Check the website to find a location near you, and to call to see if they can accomodate your dairy-free needs.