There is a direct relationship between LASIK and dry eye. All LASIK patients get dry eye at least temporarily, and many get it for longer periods or for keeps. Some get a debilitating version of it. The Dry Eye Zone's founders both have severe LASIK dry eye.
All refractive surgeries (surgeries to reduce dependence on glasses) carry some risk of dry eye, but LASIK is unique. In LASIK, a thick flap of corneal tissue is cut and the laser is applied beneath it, then the flap is replaced. This means that in addition to the nerves lost form the tissue that is ablated by the laser, nerves from at least an 8mm diameter area (excepting the area of the flap "hinge") are cut. Nerve regeneration can take a great deal of time and in some patients either never happens or is problematic.
There are also other mechanisms through which LASIK is thought to affect ocular surface and tear film health. The speculum sometimes stretches the eyelids enough to damage them, resulting in ptosis (droopy lid) and/or inadequate lid closure and excessive evaporative loss during sleep. It is thought that possibly the suction ring may somehow interfere with the goblet cells production of mucin. Finally, certain very current research is indicating that large corneal wounds (such as laser ablations, or severe epithelial defects which some experience as a complication) may result in limbal stem cell deficiency, which in turn disrupts the health of the tear film and ocular surface.
For more information specifically about LASIK dry eye, please see LaserMyEye, Inc.