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Lactose-Free Milk: Pros and Cons If you have celiac disease or a gluten sensitivity, it's important to read the label carefully to ensure that the milk or milk product you are consuming is gluten-free. Additionally, some individuals with celiac disease or gluten sensitivity may also have lactose intolerance, which is a separate condition that affects the body's ability to digest lactose, the natural sugar found in milk. In this case, lactose-free milk or milk alternatives may be a better option.