Shaykh al-Uthaymeen (رحمه الله) was asked the following question:

Question: What is the ruling on using false eyelashes for the purpose of beautification for one’s husband?

Answer: False eyelashes are not permissible because they resemble extensions, i.e. hair extensions; and the Prophet (ﷺ) has cursed the woman who artificially lengthens hair and the woman who seeks to have her hair artificially lengthened. 

And these eyelashes – if they are as I imagine; that black lines resembling hair are put onto the eyelashes to make them seem as if they are many – for (the purpose of) beautification of the eye. So if they are like this then it is counted as being from the extensions that the Prophet (ﷺ) cursed the one who does it with regards to (the hair on) her head. 

As for if the intent by eyelashes is colouring the eyelashes (i.e. mascara) then that is not prohibited.