I can highly recommend the Robicomb which electrocutes the little buggers. There are no nasty chemicals, and you don't need to leave muck on a childs hair and hope it doesn't rub off all over your house. It is also strangely satisfying to do LOL. It doesn't kill the eggs, but apparently vinegar does loosen them to then comb out a bit easier with a fine tooth comb. You can also just use the Robicomb every day for 2 weeks.

HTH