A couple of thoughts come to mind.
You could make a classic Pizza Marinara, which is a Neapolitan pizza, but using your Lehmann dough. The Pizza Marinara includes only tomato, olive oil, oregano, and garlic. No cheese at all.
Another possibility is to use a soy-based mozzarella cheese. I have used it in deep-dish pies (usually as a supplement to regular mozzarella and/or provolone) and in lasagna and, with all the other flavors and textures, couldn't detect its presence. I found the soy-based mozzarella at Whole Foods. Soy-based mozzarella is firm, mild (but pleasant) tasting, and looks very much like regular mozzarella cheese, shreds and slices just like regular mozzarella cheese, and can be used on a pizza just like regular mozzarella cheese. It will melt without any significant browning and it will be chewy and almost indistinguishable on a baked pizza from regular mozzarella cheese. However, it will not be as flavorful as regular mozzarella cheese, and certainly not as tasty or flavorful as fresh mozzarella cheese. In addition to being dairy-free, it is lactose- and cholesterol-free, so it offers clear advantages to persons who are lactose intolerant or are on low-fat or low-cholesterol diets. The hardest part may be to convince your guest to give the soy mozzarella cheese a try, even if you are able to agree on all of the other toppings to use.