It is a common misperception that lice like to jump off people's heads when they sit on a couch, they hang out there for a while until someone new sits down, and they jump onto the new head to make it their new home.
First of all, head lice don't jump. Second, while it is possible for them to get knocked off their host, they prefer to stay close to the scalp where they enjoy a warm, humid, protected environment with a ready food supply and lots of hair to lay their eggs on.(See where lice can live.)
If a louse gets brushed onto some furniture, it has just 24-48 hours to find a new host, or it will die. The chances of it being able to get back onto a host are slim. A hair strand attached to a human head would have to get close enough for it to grab with one of its six claws. And then if it isn't too weak from lack of food, it can climb the hair to the scalp and make a new home.
Female lice lay lice eggs on hair shafts, not on furniture. That's because without the egg being close to a food source (e.g. your blood), the hatched louse would have no chance at survival.
Learn more lice facts.