Cook first 6 ingredients in a saucepan over medium heat 10 minutes or until thoroughly heated.
Stir together chicken and mushroom soups and enchilada sauce in a saucepan; cook, stirring often, 10 minutes or until thoroughly heated.
Spoon one-third of sauce into a 13- x 9-inch baking dish coated with cooking spray; top with 3 tortillas. Spoon half of chicken mixture and one-third of sauce over tortillas; sprinkle with half of Cheddar cheese. Top with 3 tortillas; repeat layers once with remaining chicken, sauce, Cheddar cheese, and tortillas, ending with tortillas. Sprinkle with Monterey Jack cheese.
Bake at 350° for 30 to 40 minutes or until lasagna is bubbly. Serve with desired toppings.
*To lower sodium, choose reduced-sodium soups, canned tomato products, and cheeses.