This is exactly what essential oils based shampoos can do. You can use a tea tree oil shampoo, a lavender oil shampoo, or a coconut oil shampoo.
People around the world continue to use tea tree oil as a remedy for many. Pyrethrins and piperonyl butoxide are common ingredients in anti-lice shampoos.
We still use Paul Mitchell Tea Tree Special Shampoo and Special Conditioner, but I've seen a lot of recommendations on making your own tea tree oil shampoo