Here are some studies:
https://www.ncbi.nlm.nih.gov/pubmed/15025863 Inhibition of acetylcholinesterase by Tea Tree oil.
https://www.ncbi.nlm.nih.gov/pubmed/25756296 Essential oils in the management of the donkey louse….Conclusion: These results demonstrate that the inclusion of essential oil suspensions during grooming can be used to manage louse populations successfully.
INTRODUCTION: Pediculosis capitis is a public health problem with a high prevalence. The emergence of parasite resistance to conventional pediculicide is of great concern worldwide.
RESULTS: The results showed 100% effectiveness; short time of death, ovicidal action, activity on the adhesion of the egg, and low toxicity.
https://www.ncbi.nlm.nih.gov/pubmed/26462802 The potential application of plant essential oils to control Pediculus humanus capitis (Anoplura: Pediculidae).
https://www.ncbi.nlm.nih.gov/pubmed/22847279 Activity of tea tree oil…..on head lice
https://www.ncbi.nlm.nih.gov/pubmed/22177577 Toxicity of essential and non-essential oils against the chewing louse, Bovicola (Werneckiella) ocellatus
https://www.ncbi.nlm.nih.gov/pubmed/9439284 The potential effectiveness of essential oils as a treatment for headlice, Pediculus humanus capitis.