In a large bowl, combine the chicken, halved grapes, chopped walnuts, diced celery, and diced apple.
In a small bowl, add the mayonnaise, Dijon mustard, salt, pepper, and lemon juice, and then mix. Pour the dressing on top of the chicken mixture. Stir to combine.
Toast two slices of bread.
Add the Waldorf chicken salad on top of one slice. Close sandwich by topping with the remaining slice of bread. Repeat with other sandwiches.