I think you are in pretty good shape also.
In a way, I am glad that you picked the Lombardi's style dough to try to reverse engineer. I like its simplicity, using only flour, water, yeast and salt, and an overnight fermentation. I think that kind of formulation is a good starting point to learn the basics of pizza dough making, unencumbered by the use of additives, preservatives and conditioners. And using high quality tomatoes and cheese nicely complements the dough. To draw a comparison, recently I saw this combination of dough, sauce, cheese, and pepperoni for a major pizza chain:
PEPPERONI PIZZA INGREDIENTS:†
Crust: Enriched flour (wheat flour, malted barley flour, niacin, reduced iron, thiamine mononitrate, riboflavin, folic acid), Water, Vegetable Oil (soybean oil, soy lecithin), High Fructose Corn Syrup, Yeast, Glucona Delta Lactone, Salt, Baking Soda, Cellulose Gum, Sodium Propionate (preservative), Food Starch-Modified, Corn Syrup Solids, Vital Wheat Gluten, Dough Conditioners (L-Cysteine, ascorbic acid, enzymes), Natural and Artificial Flavors.
Contains: Soy, Wheat and Milk.
Sauce: Tomato Puree (Water, Tomato Paste), Pizza Spice (Salt, Sugar, Spices, Dehydrated Garlic, Dehydrated Onion), High Fructose Corn Syrup, Modified Food Starch, Citric Acid.
Cheese: Low Moisture Part Skim Mozzarella and Muenster (pasteurized milk, skim milk, cheese culture, salt, calcium chloride, enzymes), Powdered Cellulose added to prevent caking, Natamycin (a natural mold inhibitor).
Pepperoni: Pork and Beef, Salt, Spices, Dextrose, Oleoresin of Paprika, Lactic Acid Starter Culture, Natural Smoke Flavoring, Spice Extractives, Sodium Erythorbate, Sodium Nitrite, BHA, BHT, Citric Acid.
There's nothing I like better than reverse engineering doughs and pizzas. For me, it is challenging, intellectually stimulating and a lot of fun, especially if I am able to get close to the original product. But, what is the point of doing so with the above formulations (with all due respect to the people who love consuming the products produced by the chain in question)? If anything, I would strip out all of the chemicals that I am unlikely to be able to find in user-friendly quantities anyway, and try to get down to the basics, which I think I would have a shot of replicating at the home level. But, before doing that, I would have to do a lot of research to find out what all the chemicals are used for. That's time consuming and not a lot of fun.
BYW, the major pizza chain is Little Caesars.
Good luck and let us know how things turn out. I am confident of the modified Lehmann dough formulations I gave you but I don't know how close they will come to what you are looking for. But what I do know is that it is always possible to alter dough formulations, and dough management and oven practices as well, to achieve specific, desired dough/crust characteristics. With tons of chemicals, I wouldn't know how to do that.