Will the scar under my eyelash fade with time?

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.