I should mention that the shampoo-conditioner/nit comb method definitely works - the idea is that the conditioner makes it impossible for the lice to grip the hair shafts.
When you rinse out the comb after each stroke, you can see the lice you have removed.
I would imagine that conditioner might work, as it would effectively smother the little buggers, but it isn’t as thick, which means it would run (you’d still have to leave it in for a long time), so you may be better off with mayo. We’re going to mayo our 11-year-old this morning. Her hair is shoulder length, but very, very thick. Our oldest daughter, OTOH, has very short hair, and it’s no problem to just Robicomb/nit pick.