Can you have lice nits and no lice?

No. I did a science project on it and to have nits you need to have lice to have nits.

Yes you can, the American Academy of Pediatrics recommends that you should only treat if there is a live infestation, the presence of nit and no live bugs could be a sign of an old infection. The Company called Head Lice Heroes from Westchester, NY recommends these guide lines.