Any oil kills them, since they breathe through their skin. You need to use a lot though, and then after an hour you can wash it out and you will comb out dead lice.
We use sunflower oil (cheap organic sunflower oil is readily available to us)!
Neem oil kills them, and also repels them, but I wouldn't personally use it direct on skin except for very diluted. (Neem kills fleas too.
) Tea tree and rosemary also repel them, but neem works best IME.