We tried this and it worked perfectly. Saturate the hair with olive oil. Wait 2 (I waited three) hours. Put a plastic shower cap or impromptu one made from a plastic bag (with a young child, better to get a cheap shower cap) to keep the oil from getting on anything. At that point the lice have suffocated. I found them not quite dead after two hours. Then comb out the dead lice, wash the hair (it took me two soapings to get out the olive oil) and then pick out the nits. Even with pesticide treatments, you have to pick out the nits. Then at least twice a day, pick out the nits you may have missed, and comb out any lice that may have hatched. Apparently the lice won't have been able to lay any eggs yet, so you don't have to repeat the oil, but I did after a couple of days. Continue checking the hair for (I think it was) 10 days from the last live louse (I did two full weeks). This comes from a Harvard study and our pre-school teacher who has dealt with pesticide resistant lice in her own house.
I suggest cleaning the house thoroughly, vacuming EVERYTHING. Bag all pillows and stuffed animals for at least two weeks. (Or wash them in hot water). Change all bedding and then for the affected person/people I changed the bedding daily (probably overkill, but I was SERIOUS about getting rid of them in one shot). I also washed any clothing daily until two weeks after. I washed winter (or fall) coats as well, but not daily. Cleaning the inside of the car is important too, especially vacuming the seats.
Good luck.
After that, I have put a drop of tea tree oil in their wet hair after washing, rubbed it around and let it dry (it acts as a repellant). My children go to a school that has problems with lice from Sept.-June and we never had them again.