Fill a 9-by-13-inch baking dish two-thirds of the way with hot tap water. Add noodles, and arrange them in alternating directions to prevent sticking. Let soak while preparing sauce.
Make sauce: Heat oil in a large saucepan over medium. Add onion, garlic, Italian seasoning, and red-pepper flakes; cook, stirring occasionally, until lightly browned, about 5 minutes. Add sausage, and cook, stirring and breaking it up, until just cooked through, about 5 minutes. Add tomatoes and their puree, breaking up tomatoes with a spoon; bring to a boil. Reduce to a rapid simmer, and cook, stirring occasionally, until thickened, about 20 minutes. (You should have about 8 cups of sauce.) Season with salt and pepper.
Preheat oven to 350 degrees. Drain noodles, transfer to a baking sheet; dry dish with paper towels. Spoon 1 cup sauce in bottom of dish. Fit 4 noodles in dish (crosswise if using short noodles, lengthwise if using long), overlapping slightly. Cover with 2 cups sauce, 2 cups mozzarella, and 1/4 cup Parmesan. Repeat with another layer, then top with remaining noodles, 3 cups sauce, and the rest of mozzarella and Parmesan. Cover dish tightly with aluminum foil, and bake 1 hour.
Remove foil, and continue baking until bubbly and browned, about 30 minutes. Remove from oven; let cool 20 minutes. Cut and serve.
The lasagna can be assembled up to one day in advance. Cover with foil, and refrigerate. You may have to increase initial baking time by 5 to 10 minutes.