Heat the olive oil in a large saucepan and then add the garlic and onions and cook until softened, about 5 minutes. Stir in the tomato paste, oregano, basil and fennel, and then add the mushrooms and red pepper flakes. Stir in the ground beef and cook over medium heat until browned and crumbled. Add tomatoes and tomato sauce, bring to a boil, and then reduce the heat and simmer for 40 to 45 minutes.
Preheat the oven to 350 degrees F.
Mix together the Parmigiano-Reggiano, cottage cheese, 2/3 cup of mozzarella and the egg in a small bowl. Stir in the parsley and lemon zest.
Spoon one-quarter of the sauce into the bottom of a 13- by 9- by 2-inch baking pan.
Place 3 uncooked lasagna noodles on top of the sauce without overlapping. Spread half of the cottage cheese mixture over noodles and top with another one-quarter of the sauce. Repeat the layers, ending with sauce, and sprinkle over the remaining mozzarella cheese. Bake for 45 minutes. Let rest 10 minutes before serving.