In season 16, episode 14 - Cooks Illustrated/America's Test Kitchen gives a recipe for Thick Crust Sicilian Pizza.
At the beginning of the show, they visit L&B Spumoni Gardens and, at least in theory, the ATK pizza is modeled on the L&B.
I mention this because I noticed that in the last few messages, there is mention of the cake like crumb, etc. In "Why this recipe works", the Cooks Illustrated people say:
"In order to create a Sicilian pie with a creamy, golden interior and a delicate, crisp bottom, we use a mixture of semolina and all-purpose flours. To give it a fine-textured, almost cake-like crumb, we use a three-pronged approach. We use a generous amount of olive oil in the dough to tenderize it, we cold-ferment the dough overnight to let flavors develop without large bubbles forming, and then we roll it out and weigh it down with another baking sheet during the final proof to keep the crumb even and tight.
I have made this recipe and found it to be an excellent pizza. I have no idea if it is similar or not to L&B. FWIW, here is the recipe:https://www.kcet.org/food/weekend-recipe-thick-crust-sicilian-style-pizza