Well, head lice only get on clean people so that's a plus, right? Body lice like dirty people. Head lice won't stay on dirty hair, they can't survive in it. So at least you know the kid is pretty clean. Mom is probably bathing her and doing what she can.
Sounds like you need to do some research on head lice. They don't go away in one visit with you. She has them in her clothes, they are on your car seats the moment she gets in and sits down, they are on your furniture, anywhere she sits or lays down they crawl off.
So you have a problem with them too. And those old wives tales are just crazy wrong.
Please go to places like headlice.org and read good advice on how to get them taken care of.
Hair treatments do NOT get rid of them. They are pretty much immune to those now. Sprays, powders, all that stuff they want to sell you are just empty cans of stuff that make no difference.