Mayonnaise tries to kill head lice by suffocating them, but lice are able to close their spiracles and hold their breath, so they come back. Researchers have developed a lotion that stuns the spiracles open, so the mineral oil and other inactive ingredients can soak the lice and suffocate them once and for all. It's better than conventional medications, because you don't have to pour poison on the kid's head. The stuff is Benzyl Alcohol Lotion 5% (the brand name is Ulesfia). I wonder if it kills nits, too.
A couple of years ago, there was a study showing that a really heavy duty hot-air blower could kill an infestation in 30 minutes, including the nits. It dries them out. I haven't heard anything about it since.