Thank you for your query,
Pulling eyelashes is called Trichotillomania
It is a habit disorder
Children with repetitive hair pulling have an increasing sense of tension immediately before pulling or when resisting the behavior, followed by pleasure or relief when pulling out the hair.
Usually it subsides spontaneously.
If it persists more than 6 months it requires behavioral treatment.
Medication like fluoxetine will be useful.
So consult your Pediatrician
or Child psychiatrist
for further evaluation and management.
Hope I have answered your query.