The study was done with “mitochondrial DNA from the two modern types of lice”, i.e., living lice. DNA is made up of a number of complex molecules, and of biological origin, so it will break down, or get eaten by something microscopic. Some DNA fragments have been found that go quite far back, but even in purposely preserved remains (such as Egyptian mummies) it’s hit or miss whether analyzable quantities survive. Often the samples that are best come from tooth pulp. The Heidelbergensis sample analyzed in the 1990s was mtDNA, and consisted of fewer than 400 base pairs out of a presumed original number of over 16,000. Those remains were much older than Egyptian mummies, much older than Oetzi.
Two? I guess they consider the head louse and body louse subspecies of Pediculus humanis. Pthirus pubis* isn’t extinct yet, albeit vastly reduced in numbers due to modern grooming practices.
*try saying that fast 3 times after a couple of drinks.