Hi, in general, the answer is no.
The concern is that patients with Sjogren syndrome have very dry eyes, and LASIK (or any other laser refractive surgery including epiLASIK/PRK/TransepiLASIK/TransPRK/SMILE etc) will make the dryness worse.
It's worth remembering that dry eyes span a spectrum from mild to severe, and mild dry eye not related to Sjogren syndrome is not a problem for LASIK.
On the other hand severe dry eye, even if not Sjogren related, may 'disqualify' a patient from laser refractive surgery because of the risk of delayed epithelial healing, blurred vision after surgery, corneal inflammation, etc.
Even if a patient with Sjogren syndrome does not currently have very dry eyes, there is a high chance of developing this later on and experiencing problems as mentioned above. Hence laser refractive surgery is not appropriate for patients with Sjogren syndrome.