The issue we had with effective anti-lice treatments of our kid's heads was that their contents are either highly toxic (Lindane) or highly allergenic (Pyrethroid) if tested and approved as a medical product. In addition more and more lice are becoming resistant to these drugs.
Other non-pharmaceutical remedies were not proven to be efficient, at least they were not tested in large studies as needed for official approvements as a drug.
Nevertheless we succeeded to entirely get rid of lice several times by using a shampoo preparation available from our local drug store containing a mix of coconut oil and the silicone oil dimeticone.
We had to follow the instructions closely, i.e. two applications of the shampoo each followed by 30 minutes tight enclosure of the shampooed hair in a plastic shower cap before rinsing. This had to be repeated after a week to also get rid of new lice that may have hatched from remnant vital nits.
We used a similar preparation for washing the bed linens and clothes too in order to also get rid of lice or nits there (but this was only for us to feel comfortable, we did not see any nits or lice outside the heads of our kids).
The containing oils are supposed to suffocate both, the insects, and their nits.
The shampoo will not remove the dead nits still tightly attached to the hair. We could impossibly comb the long curly hair of our girl using a nit-comb, it hurt too much. In addition how long we tried to remove nits with the comb they would still remain attached to the hair in large numbers. But still, after the shampoo treatments had been repeated after a week the remaining nits obviously were dead as we did not observe any further vital lice and the dead nits disappeared gradually over some weeks.