Will the scar under my eyelash fade with time?

At this point the incision is expected to be reddish and noticeable.  They are immature and as they mature they become more fine and lighten up.  These incisions usually heal very well over time. Give it a few months. Best wishes. 

Four weeks is too early to pass judgment on incision after lower eyelid surgery including a mid facelift.

Healing takes several months and you should notice that the scars will slowly improve.  The skin under the lashes usually heals very well, so I would not be worried at this point.

4 weeks is very early.  Collagen in scars is deposited, degraded, and remodeled.  The remodeling phase of wound healing, or scar maturation, can take over a year.  Tensile strength of wounds approaches 80% near 8-12 weeks.Typically, scars take time to fade and visibility improves significantly after 4 weeks.  Less often, poor scar formation necessitates intervention.  I have my patients avoid the sun, start massage, and use a silicone based scar product (making sure they don't get this in their eyes of course).  Check with your board certified plastic surgeon to evaluate your scars.

Eyelid skin is very thin and very well vascularized (has very good blood flow). The benefit of this is that incisions in the eyelids typically heal very well with little to no stigma of previous surgery. Everybody heals at his or her own unique pace and it can take a few months for incisions to completely heal. It is important to be patient with the healing process and make sure that you are compliant with you surgeon's post-operative instructions. Follow up with your surgeon to ensure that you are healing according to plan.

Four weeks is a very short postop period and the scars are in their inflammatory phase.  The scars should go on to heal very nicely and continue to follow up with your plastic surgeon. Best wishes.

Eyelid surgery scar usually heals very well with minimal scarring. It can take few weeks to few months o improve the scars. Ensure that you followup with your surgeon for any advice on improving the scar such as massage, scar creams etc