I'm surprised no one has mentioned Dr Bronners peppermint castile soap for Lice. You have to use the peppermint one though because the peppermint and saponified oils kill the lice. It's used as a natural insecticide in organic gardening.
What you do is you use the Dr Bronners straight undiluted. Apply it generously to dry hair. You do not have to bag it. The soap dries and won't get on your stuff. Even if it does its just soap. Bagging a childs head is a suffocation hazard, I know alot of parents mean well and think it wont happen to their kid but this is more common than you think. So you get a bit of soap on your kids pillow, ITS NOT THAT SERIOUS. Leave the soap in all day or overnight, when you take your kid a bath and rinse it out make sure not to get it in their eyes because the peppermint stings. It's harmless but why make them more uncomfortable. A bunch of dead lice will be falling out of their head after doing the treatment.
Do the UNDILUTED treatment every few days (use your best judgement as you know how bad the infestation is), everyday when you bathe them use the dr bronners diluted as a shampoo and when their hair is dry add coconut oil as a leave in treatment. You can even add peppermint oil to coconut oil but its not necessary. Coconut oil does plenty on its own. You should nit pick but you dont have to. My daughter is autistic and its hard to get her to sit still for it. Also if you miss even one egg and it hatches your efforts were for nothing. Use dr bronners and the coconut oil religously and you will keep killing them as they hatch and youll be lice free before you know it. Use the dr bronners diluted as a shampoo, then use the coconut oil as a leave in treatment. No nit picking necessary. Though if you do a vinegar rinse after shampooing and comb with the nit comb it will help take the eggs out but you can just comb, you dont have to sit there for hours nitpicking. Just comb it through their hair and youll get some eggs out here and there. This is how I rid myself and my daughter of lice without nitpicking through our hair and our family and friends have also has success with the Dr Bronners. I normally notice theyre all gone after 1 or 2 treatments (you might find babies that have hatched after the first treatment). But I keep shampooing for 2 to 4 weeks as a precaution. Washing with Dr bronners regularly and using the coconut oil kills them as they hatch and keeps them from laying more eggs. So even if you are nitpicking and miss some eggs they wont live long enough to mature and lay more. And remember to use the Undiluted treatment every few days as a more heavy duty treatment. Its the most important one.
On another note PLEASE DO NOT USE KEROSENE on your child's head to get rid of lice. All it takes is some static on your childs clothes to light the kerosene and their head on fire. It's very dangerous. I understand lice suck and they are a plague on our children but at the end of the day they are harmless bugs. You don't need to practically douse your childs head (or yours) in gasoline. ITS NOT THAT SERIOUS.