If you have a dairy allergy, is your chances of being lactose intolerant higher?

No: Lactose intolerance is a inherited metabolic problem in that the intestine lacks the enzyme to break down the lactose in milk. Milk allergy is also partly genetically predisposed but is not linked to lactose intolerance. There is a remote possibility that if the intestine gets inflamed enough by continuing exposure to a food allergen, the inflammation may lead to a transient lactose intolerance.