Can hair transplant and eyelid surgery be done at same time? If not which should be done first? (photos)

Most of the time the answer is NO.  Hair transplant and eyelid surgery are two completely different type of surgeries.   Theoretically, if you have post surgical swelling around your eye after a hair transplant surgery, eyelid surgery would be an issue.

Many people following a hair transplant will develop swelling in the forehead and a few might swell into the eyelids. I generally recommend that the two procedures be separated in time. Either the eyelid or the hair transplant surgery can be first, but wait 2 weeks between them because if you are one of those few people who develop swelling in the eyelids after a hair transplant surgery, then if they are done at the same time, it might not give you the best outcome. See web reference below for hair transplant lowering procedures on four women

Yes you can do both on the same day.  The hair that is harvested from the donor area can be used for both and it is actually more convenient for the patient  to do on the same day.