Spoon 1/2 cup enchilada sauce over bottom of a greased 4-qt. slow cooker. Add enough tortilla pieces to cover sauce.
Stir together chicken, sour cream, 2 cups cheese, and soup. Spread 2 cups chicken mixture over tortilla pieces. Top with tortilla pieces to cover. Drizzle with 1/2 cup enchilada sauce. Repeat layers twice, ending with tortilla pieces and remaining enchilada sauce. Sprinkle with remaining 1 cup cheese.
Cover and cook on Low 4 hours. Place lettuce on plates; top with chicken, beans, and tomatoes. Serve hot.