@ddljohn-- Tea tree oil is toxic for pets, so do not use it! Most essential oils are not safe to use on pets.
When my dog had lice, I just took her to the vet who gave a medicated shampoo and a topical treatment. We washed her with the shampoo once a week for a month and used the topical treatment daily. It worked, it cleared up the infestation.
The more difficult part was cleaning the carpets and her bedding because the vet said their eggs must be in the environment and the lice can come back. We used borax to clean the carpets and I washed her bedding and blanket is very hot water and some bleach.
I guess all this worked because the lice haven't returned. I think we were lucky because I heard that lice in dogs is very hard to get rid of.