Preheat your oven to 400°F. In a large skillet, cook the sausage and onion over MEDIUM heat, breaking the sausage into small crumbles. Cook until the sausage is no longer pink and the onions are soft, about 5–7 minutes.
Add to the skillet the crushed tomatoes, tomato sauce, dried basil, 1/2 teaspoon of black pepper, and salt. Bring the mixture to a boil, then reduce the heat and let it simmer uncovered until slightly thickened, about 10-15 minutes.
In a separate bowl, whisk together the beaten egg, ricotta cheese, 1-1/4 cups of Parmesan cheese, and the remaining 1/4 teaspoon of black pepper. This will be your rich and creamy cheese layer.
Spread 1-1/2 cups of the meat sauce along the bottom of a greased 13×9-inch baking dish. Place 4 no-cook lasagna noodles over the sauce. Over the noodles, spread 1-1/2 cups of the ricotta cheese mixture, then sprinkle 1-1/2 cups of mozzarella cheese.