Lice and their eggs can be suffocated, but it takes several hours.
Easiest way to be rid of lice is to douse the entire head, scalp to tips, with a dimethicone-containing shampoo. No water -- just lots and lots and lots of dimethicone-containing shampoo. Then let it sit -- do not rinse it out -- for 6-8 hours. Then rinse it out very thoroughly.
Dimethicone is most commonly found in shampoo/conditioner combos like Pert. Dimethicone is not a poison ... but it is a pernicious lubricant. It will cover the individual lice and their eggs completely and not slip off or rub off. This cuts off the oxygen supply, which doesn't kill the lice/eggs instantly. Takes several hours. But it will work, and the lice never can develop immunity.
Some other substances, such as mayonnaise, can do the same thing. Mayo is very hard to clean out of hair, though. Just get some Pert and make it easy.