Divide the dough in half. Roll each half into a 12-inch circle, about 1/2-inch thick. Press the dough into 2 greased 12-inch deep-dish pizza pans. Cover with a clean dish towel and let rise 30 minutes.
Preheat the oven to 400 degrees F.
In a large saute pan, over medium heat, add 2 tablespoons of the olive oil. When the oil is hot, add the onions. Season with salt and pepper and saute for 2 minutes. Add the peppers, season with salt and pepper, and continue to saute for 3 minutes. Remove from the heat. Transfer to a bowl and set aside.
In the same pan, over medium heat, add the sausage and render for 4 to 6 minutes. Remove and drain on paper towels.
Lay 1/4-pound of the sliced provolone on the bottom of each pizza. Spoon 1/2 the onion and pepper mixture over each pizza. Sprinkle 1/2 of the sausage over the onion mixture on each pizza. Scatter 1 cup sliced mushrooms over sausage. Spread 1 cup of the tomato sauce over the top of each pizza. Layer 1/4-pound mozzarella slices over top of each pizza. Drizzle with remaining olive oil. Bake the pizzas for 25 to 30 minutes or until golden brown.
Remove the pizza from the oven and cut into individual servings.
In an electric mixing bowl, whisk the yeast, sugar, water and lard together to make a paste. Add the flour and salt and mix, using a dough hook, until the dough comes away from the sides and crawls up the dough hook. Remove the dough from the bowl. Grease the bowl with olive oil and place the dough back in the bowl. Cover the bowl with plastic wrap and let the dough rise until doubled in size, about 1 hour. Turn the dough out onto a floured surface and divide dough in half. Roll the dough into balls, cover, and let the dough rest for 15 to 20 minutes. The dough is ready to be shaped.