LASIK, and any other type of ocular surgery, CAN cause the eyelids to droop. This is a (rare) complication called ptosis. It is thought to be a possible side effect of the eyelid clamp used to keep the eye open. With cataract surgery (not LASIK), studies have shown a risk to be generally less than one percent. Note that hard and rigid contact lenses can also cause this. Ptosis is a change in position (a dropping) of the eyelid margin. If you are describing more skin and fat overhanging the lid margin, with no change in the lid margin position itself, you are describing a different condition called dermatochalasis. There is no known association between LASIK and dermatochalasis. The treatment for dermatochalasis is blepharoplasty, commonly known as an "eye lift." This is very different from ptosis repair, which will alter the position of the lid margin itself.