Cook the turkey in a large saucepan coated with cooking spray over medium heat until browned, stirring to crumble. Add water and pasta sauce; bring to a boil. Cover, reduce heat, and simmer 10 minutes. Remove from heat.
Combine 2 cups mozzarella, cottage cheese, and next 4 ingredients (cottage cheese through pepper) in a bowl.
Spread 1 cup turkey mixture in bottom of a 13 x 9-inch baking dish. Arrange 3 noodles over turkey mixture; top with 1 1/2 cups turkey mixture. Spread half of cheese mixture over turkey mixture. Repeat layers, ending with the remaining turkey mixture.
Cover and bake at 350° for 1 hour. Sprinkle with 1 cup mozzarella cheese, and bake, uncovered, for 10 minutes. Let lasagna stand 10 minutes before serving.