Could dry eye and dry mouth be related? Is there any disease associated with the two?

Sjogrens Syndrome. There are many causes of dry eyes and dry mouth. One such syndrome sjogrens syndrome, people have dry eyes and dry mouth. It is considered an autoimmune disease. You should see your doctor to get the correct diagnosis and treatment options.
Yes. Those two can be associated with a disease called sjorgrens syndrome. Dry eyes, dry mouth are very common with this. Patients need eye drops and saliva substitute.
Yes. Sjogren's syndrome causes dry mouth & dry eyes. Ask your medical specialist about testing you for this condition.