Yes, anything will die if it ingests enough of those products, but lice can survive being submerged in water for 8+ hours and are very resilient. It isn’t very healthy to leave poisonous products on anyone’s, especially children’s heads, and can be life threatening.
If you want to get rid of lice, the only proven safe and effective home remedy is manual lice combing until you remove every live bug and nit. It takes a professional about 1.5 hours to do an adult with shoulder length hair.
For someone new to lice combing and without an professional hair experience, you can expect to comb each person for about 1 hour every day for 1-2 weeks or more depending on how methodical and consistent you are to get fast results.
Many of our clients have spent that time or longer before deciding to hire a professional and get peace of mind from knowing it is completely take care of in one day.