What is the ruling on using natural oils to lengthen hair and thicken eyelashes?

There is no objection to using natural oils, such as castor oil, to lengthen hair, provided they are free from unlawful substances like pork and alcohol, and that their use does not harm the hair or body. This also applies to thickening eyelashes. The basic principle regarding things is permissibility unless there is evidence prohibiting them.