Bring a large pot of salted water to a boil. Add the lasagna noodles and cook until al dente. Strain the noodles, reserving 1 1/2 cups of the cooking water, and toss with olive oil, to keep them from sticking. Let cool.
Meanwhile, heat the oil, sliced garlic, red pepper flakes and 1/2 teaspoon salt in a large skillet over medium heat. Stir as the oil heats up; once it shimmers, add the tomatoes and reserved cooking water. Bring to a high simmer and cook, stirring occasionally, until the sauce thickens slightly and the water has evaporated, 15 to 20 minutes. Remove from the heat and let cool to room temperature.
Combine the beef, pork, breadcrumbs, onions, grated garlic, tomato paste, Worcestershire, 2 of the eggs, rosemary, 1 1/2 teaspoons salt and 1/2 teaspoon pepper in a large bowl. Use your hands to thoroughly combine.
Combine the ricotta, 1 1/2 cups each of the fontina and mozzarella, Parmesan, parsley, the remaining egg and 1 teaspoon salt in a medium bowl.
Position an oven rack in the center of the oven and preheat to 350 degrees F. Lightly grease the bottom and sides of a 9-by-13-inch baking dish with oil. Spread a few tablespoons of sauce on the bottom of the dish. Cover with 6 overlapping noodles and top with 1/3 of the sauce, 1/2 the meatloaf mix (crumble over top and pack down) and 1/2 the cheese mixture (dollop over top and spread out into an even layer). Continue to build with the noodles, sauce, meatloaf mix and cheese to make two more full layers. Top with noodles and finish with sauce.
Cover loosely with foil and bake for 45 minutes; uncover and continue to bake until the meatloaf is bubbly and reaches an internal temperature of 165 degrees F, 15 to 20 minutes more. Uncover, sprinkle with the remaining 1/2 cup each fontina and mozzarella and bake until the cheese melts, about 5 minutes. Remove and allow to rest for 10 minutes. Cut into squares and serve.