The short answer to your question is: No,there are no lice that can be passed from humans to pets, or vice versa!
Lice are very species specific, which means that human head lice only like humans, cow lice only like cows, and so on. Lice in dogs is very rare - in 14 years of practice I have never seen it! The louse simply will not stay on a species other than the one it usually infests. Animals will get lice from direct contact with another animal (same species) with lice, OR from contact with a contaminated comb, brush, etc. The nits (eggs) on the brush will infest the other animal of the same species.
I have been a vet for 14 years, and worked with animals for about 10 years before that...and have never seen lice on cats or dogs, though it can happen.
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The above is given for information only. Although I am a licensed veterinarian, I cannot legally prescribe medicines or diagnose your pet's condition without performing a physical exam. If you have concerns about your pet I would strongly advise contacting your regular veterinarian.
Best wishes to you both,