All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
Fixing artificial eyelashes is included in the prohibited fixing of hair extensions. It also implies changing the creation of Allah Almighty. In a Hadeeth, the Prophet, sallallaahu ‘alayhi wa sallam, cursed women who fix hair extensions and those who have hair extensions fixed for them. [Al-Bukhari and Muslim]
Moreover, Allah Almighty told us that Satan had pledged to mislead mankind and order them to change the creation of Allah. Allah says through the words of Satan (what means): {And I will command them so they will change the creation of Allah.} [Quran 4: 119]
Thus, Muslims have to avoid this action.
Allah knows best.