Upper and lower eyelid surgery scars are among the best scars a patient can receive, IF the surgeon uses precise technique, fine sutures, proper incision location, and the patient follows post-op directions well.
Upper eyelid incision are hidden by the lid fold (except in Asian patients, who may not have this fold). Care must be taken by the surgeon to not go too high, too low, or too far laterally near the crows-foot area, or the scar may be more visible. Likewise, too much skin removal can cause excessive tension on the closure and affect healing adversely. I mark and measure my patients pre-operatively while upright and alert (no medication or sedation on-board) to determine the accurate true amount of skin excess to remove. Finally, the choice of suture material and closure technique can influence the scar's quality. I use a very fine (6-0) monofilament nonabsorbable suture woven from inside the skin incision edge to the other side of the skin incision edge (subcuticular closure) and left in one piece for both lids. When it is ready to be removed in a week or so, I simply slide the suture from the skin by pulling from the center where the stitch is exposed. Minimal discomfort, no cross-hatch marks, great scar (but somewhat more difficult to do). Many surgeons simply use an easy over-and-over baseball stitch and remove it before it leaves (bad) marks, but it can leave tiny suture hole scars or cross-hatch marks if it is too tight, left in too long, or if the patient has more swelling than "average." Sleeping with your head elevated above heart level for at least two weeks helps keep swelling to a minimum. The same goes for avoidance of lifting, straining, or vomiting after surgery!
Lower eyelids are even more tricky to do well, and even skilled, experienced surgeons can have difficulties with proper tension, lid position, and scarring (not just the visible skin scar, but the ones beneath the surface that can pull or distort the lid during healing). At least the skin scar can be virtually invisible, if the scar is placed just below the eyelashes--not several millimeters below, which I commonly see (to avoid cutting the eyelashes, or just out of habit), but adjacent to the eyelashes. This is hard to do properly and involves utilizing a pointy scalpel blade directed from below the skin upwards, which allows the surgeon to place the incision much closer to the eyelashes, giving a scar which heals better than virtually all others. When I use this special technique for external lower eyelid incisions, I use very tiny absorbable sutures for closure. These dissolve within a week, do not leave a mark, and do not require trying to decide what is an eyelash and what is a suture (for removal). Of course, if you only have a tiny amount of fat to be removed, the incision can be hidden inside the eyelid, and this is completely invisible. But this incision does not allow any lid tightening or skin/muscle smoothing.
Even with "standard" methods, eyelid scars heal beautifully for the vast majority of patients and surgeons, usually even if you form bad scars elsewhere. But with these tips and techniques, I believe scars can be even better.