Can gluten/lactose intolerance cause hypothyroidism?

No: Although fatigue is often associated with gluten intolerance, it has nothing to do with the thyroid.

Thanks for asking!: Celiac disease, which is gluten intolerance (not lactose intolerance) can be associated with thyroid disease and other auto immune disorders. Patients with celiac disease, especially when not on gluten free diet can have lactase deficiency and therefore lactose intolernace. Some patients with treated celiac disease can have lactose intolernace due to lactase deficiency, jus like any other person.