Below are some resources about lice, including treatment options and prevention techniques, from the Centers for Disease Control and MuskegonHealth.net. The latter has instructions for an oil-based treatment.
The CDC does not recommend using this treatment as an alternative to a specialized shampoo but possibly in conjunction with a shampoo.
Some who object to the insecticide in the shampoos or for whom no shampoo has proven effective have seen success with the oil-based treatment.
No matter what treatment is used the most essential steps are the systematic removal of every nit and repeating the treatment in 7-10 days (see instructions for specifics).