Thanks to viewer Todd for this recommendation:
"I am lactose intolerant and get a great cheeseless/dairy-free pizza from a place called County Inn Pizza, 12049 Roosevelt Rd Elmhurst, IL (20min west of Chicago). They stated that there is no dairy products in either the pizza dough or pizza sauce. I recommend the County Inn special no cheese."
We couldn't find a website for them, but their phone number is: (630) 832-9382