It should! It killed my dogs fleas, and my cat's mites. I'd try it any way! Say, Zap daily for a few days, maybe even a couple or three times a day. (full sessions). lice will come back easily, so make sure you do all the cleaning procedures while zapping.
I believe you can sprinkle borax powder on the carpet and furniture, then vaccuum it up, but diatamatious earth might be better. (You might want to check into these (I have not tried them myself) - The skin parasite
forum might have some tips for this too.
Hope this helps