Heat oven to 375°F. Coat 13 x 9 x 2-inch glass baking dish with nonstick cooking spray.
Combine chicken soup and 2/3 cup milk in large bowl. Spoon 1/4 cup of milk mixture over bottom of prepared baking dish.
Add chicken and corn to remaining soup and milk mixture in bowl.
Stir together the ricotta and mozzarella cheeses in another large bowl.
Place 3 noodles over soup mixture in bottom of baking dish. Top with half the ricotta mixture, another 3 noodles, the chicken mixture, another 3 noodles, the remaining ricotta mixture and another 3 noodles. Mix together the tomato soup and the remaining 2/3 cup milk in a small bowl. Pour over the lasagna noodles in baking dish. Sprinkle evenly with the Parmesan. Cover baking dish with aluminum foil.
Bake in 375°F oven for 30 minutes. Remove foil. Bake 15 minutes longer or until bubbly around the edges. Let stand 15 minutes before serving.