There are probably more species of parasitic animals than all the other animals taken together. I say probably because we haven’t counted all the animals: we don’t know how many there are. But almost every animal you examine close enough has at least one dedicated parasite. Humans, for instance, have at least three obligate ectoparasites: the head louse, the body louse and the crab louse. That is not couting the numerous parasited we share with other animals, like the flea, several mites, all kind of worms, tapeworms, nematodes, etc. etc.
There are roughly 5,000 species of lice described, with 4,000 parasitizing birds and an additional 800 special parasites of mammals worldwide. Considering that there are about 10,400 extant species of birds lice alone are enough to provide a dedicated parasite for every two species of bird (plus the mites, the fleas… you get the idea).
Lice are so attached to their hosts that they can be used to confirm other theories about when humans and chimpanzees diverged or when humans first arrived to America.
Parasites can also be used to gauge the health of an entire ecosystem: as many parasites require multiple hosts during their life cycle they will disappear among the first if only one of the hosts in the chain becomes rare.
And coming back to the Iberian lynx: when in 2002 there were only 94 left in the world they were all captured to start a conservation and breeding program. They were de-wormed and washed. They will get their worms back, no problem, they get them with the diet. But the lynx lice that were their specific parasite are probably gone for good. They will still occasionally get some lice from other animals, from the rabbits they mostly eat, or from birds. But the lice won’t like it very much and will jump ship as soon as they can.
They will still get ticks, though.