Add mayonnaise, apple cider vinegar, ground black pepper, garlic powder, sugar, prepared horseradish, salt, and lemon juice to a medium-sized bowl and whisk until fully combined. Add a pinch of cayenne pepper powder if you would like to add a little spice to the sauce.
Add your Alabama white sauce to a sealed container and store in the refrigerator for around a week or so.
Serve on smoked and/or pulled chicken or even grilled chicken pieces. It's also a great addition to store-bought rotisserie chicken.