Cook the sausage in a large skillet over medium heat. Transfer to a large bowl and pour out excess grease.
In the same pan, heat the olive oil and cook the onion until soft, about 4 minutes. Add the garlic and cook 2 minutes more. Add the crushed tomatoes, oregano, crushed red pepper, salt, and pepper, and return the cooked meat to the sauce. Simmer 15 minutes until slightly thickened.
Combine cottage cheese and 1 cup mozzarella in a medium bowl. Mix in the egg and 1/4 teaspoon of each salt and pepper.
Preheat oven to 350 degrees. Brush a 13 x 9 pan with olive oil. Layer 1 cup of the tomato sauce on the bottom, 1/4 of a cup of the cheese, 1 tablespoon of the parmesan, and 3 lasagna noodles. Repeat 3 more times. Sprinkle the top with 1 cup of shredded mozzarella and the remaining tablespoon of parmesan cheese.
Cover tightly and bake covered for 30 minutes, then remove the foil and bake 15 minutes more. Let stand 15 minutes before serving.