No, vinegar does not kill lice.
More Info: Female lice use a very hard substance similar to cement to attach their eggs, known as nits, to the hair shaft. Though vinegar does not kill lice, there are a few extension services that suggest rinsing hair with vinegar to help loosen the hard substance that holds lice eggs tightly to the hair.
Lice do not survive long off the hair of their host so the most effective first line of defense when faced with a lice infestation is to physically remove the nits with a special comb. Once all lice have been removed the infestation needs to be managed by washing anything that the individual has come in contact with at a temperature of 130-140 degrees for a minimum of ten minutes and dried on the highest heat setting for twenty minutes.
Lice are more prevalent in children and prefer longer hair. The primary way to kill lice is with specially formulated lice killing shampoo, and the removal of knits is best done by hand with a metal comb.