How to kill head lice and most importantly the eggs?

Chemical Tx . We use Malathion and permetrin topically and it is important to use a fine comb to remove all the nits.
Lice not Nice. Tx of lice requires accurate identification of nits & lice. A pediculicide is usually used- OTC like Nix or RID or prescription meds like lindane or malathion. Work carefully through hair & remove individual nits. Purchase a special lice nit comb to aid you. Check for nits & remove as seen over the next 7 to 10 days. If there are nits after 7 to 10 days – a 2nd pediculicide tx may be needed.
Shampoo and comb! A thorough shampoo with l% Permethrin (nix) is the most effective over-the-counter treatment. This should kill all the live insects. Then it is very important to use a fine-tooth comb through the hair and remove all the tiny white eggs (nits). These may hatch later if not removed, and start the problem all over. There are also stronger prescription drugs that your dr. May recommend.