All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Plucking out or shaving the eyelashes is included in the prohibited Nams (prohibited removal of facial hair). In Muntaha Al-Iradat, it is stated: "Nams is prohibited, it means plucking out the facial hair." In Al-Muhalla, Ibn Hazm said: "Plucking the facial hair is prohibited. Thus, a woman who does so for herself or for others is cursed by Allaah Almighty."
However, if long eyelashes cause harm to the eyes, then it is permissible in such a case to trim a portion whereby the harm is removed.
Allaah Knows best.