Spread mayonnaise on one side of each slice of toast and cut into small pieces. Arrange toast, mayonnaise side up, in a greased 8" square baking dish. Top with cheese slices and bacon. In a skillet, fry eggs over medium heat until completely set; place over bacon. Top with tomato slices; set aside.
In a sauce pan, melt butter. Stir in flour, salt and pepper until smooth. Gradually add milk. Bring to a boil; cook and stir for 2 minutes or until thickened. Pour over tomato. Sprinkle with cheddar cheese and onions. Bake, uncovered, at 325 for 10 minutes. Cut into squares; serve with lettuce.