Gluten and Dairy-Free Waldorf Salad (No Nuts)

As you can tell by the title of this post, we have food allergies at our house. Some of us are allergic to pecans; some can't eat walnuts; others are lactose and gluten intolerant. So how do I make a gluten-free, dairy-free, nut-free Waldorf salad? Here's my recipe:

Ingredients:

4 apples -- cored and diced
1/4 cup chopped celery
1/2 cup raisins or dried cranberries
1/2 cup mayonnaise
1 Tbsp. sugar
1 tsp. fresh lemon juice
dash of salt

Directions:

1. Mix mayonnaise, sugar, and lemon juice in a bowl. Add salt to taste. 
2. In another bowl, toss apple, celery, and cranberries. 
3. Fold mayonnaise mixture in with a spatula and stir until apples are well-coated.