Yes, people with Grave's Disease can have LASIK surgery. People with Grave's disease tend to have a higher incidence of dry eyes and ocular surface inflammation, both of which need to be controlled adequately before proceeding with surgery and followed closely and treated aggressively after the surgery.
Some patients with Grave's disease can have eyelid closure abnormalities with resultant corneal exposure and severe corneal dryness, in these patients LASIK surgery is usually not indicated. Some patients with Grave's disease have double vision due to ocular misalignments and eye muscle dysfunction, it is important to understand that LASIK surgery will not correct this situation.