Since you mention them together a few times, I think it is worth pointing out that the vast majority of lactose intolerant people simply lack the ability to produce an enzyme that digests lactose, while gluten related conditions mostly seem to involve some sort of immune response. Some people probably do have a genuine milk allergy, but mostly lactose intolerant people are just unable to make lactase.

The discomfort stemming from lactose intolerance comes from bacteria digesting the sugar and making gas, etc. The discomfort (and further problems) from gluten is well understood to be an immune response in some instances (Celiacs, wheat allergies), and still thought to be an immune response in most remaining cases.