The short answer is no. Lice are species specific. That means that human lice affect humans and dog lice affect dogs. Dogs and cats have higher basal temperatures than people usually running at 101 to 102.5 degrees F. Human lice don’t thrive at the higher temperature and don’t prefer cat and dog blood which they need to feed on.
Your pets don’t need to be treated since the lice won’t lay nits (eggs) on your pet’s hair. However, if someone with head lice were to hug your pet and a louse were to crawl on your pet’s fur, re-infestation might occur within 24 hours since lice may survive on your pet for a day. Best to skip the hugs until the coast is clear.