Cook and drain lasagna noodles as directed on package; place in cold water to cool.
Meanwhile, in 4-quart saucepan or Dutch oven, cook beef, sausage and onions over medium-high heat 5 to 7 minutes, stirring frequently, until beef and sausage are thoroughly cooked; drain. Stir in tomatoes, tomato paste, basil, sugar, oregano, salt and garlic powder, breaking up tomatoes. Heat to boiling. Reduce heat to low; simmer uncovered 30 to 45 minutes, stirring occasionally, until very thick.
In medium bowl, beat eggs. Stir in ricotta, cottage and Parmesan cheeses and parsley; set aside.
Heat oven to 350°F. In ungreased 13x9-inch (3-quart) glass baking dish, spread about 1/2 cup beef mixture. Top beef mixture with 3 noodles, half of the cheese mixture, half of the remaining beef mixture and half of the mozzarella cheese. Repeat layers, starting with noodles and ending with mozzarella cheese.
Bake 35 to 45 minutes or until lasagna is bubbly and top is golden brown. Cover with foil; let stand 10 to 15 minutes before serving.