No, it may share the same symptoms, but milk allergy is not the same as lactose intolerance. Lactose intolerance is the inability of the digestive system to break down lactose because of low or inexistent lactase enzymes. Milk allergy is an immune response to milk and milk products, most common in cow's milk. Milk allergy is also noticeable in the first year of life. Lactose intolerance is more prevalent after infancy and may persist until adolescence and adulthood.