Thanks to JeffB’s cites from the OED, we see that exaltation of larks predates pride of lions. Both terms are of similar antiquity and from the same tradition, that of venery (hunting). These do, in many cases, represent fanciful coinages, in part due to the need of the aristocracy to validate their superiority by deveoloping technical terms for every aspect of aristoratic pursuits such as hunting. But the only real difference between them is that pride of lions has survived in general use, and exaltation of larks has not. Actually, the coiners of the terms were probably far more familiar with the hunting of larks (which were used as food during that era in England) than they were in hunting lions. And “exaltation” is an entirely appropriate term to use for larks, which fly high in the air in their courtship display. While I’m not sure of its antiquity, “murder of crows” may very well refer to their liking for carrion and thus battlefields and other scenes of slaughter.
My guess is that very few of these collective terms predate the 1400s (these being herd, flock, pack; though according to the OED “flock of seagulls” is a relativly recent usage. And I wonder how far back “school of fish” goes - akthough I believe it’s probably derived from “shoal.”)
There are rather few collective terms that are used by naturalists. Herd serves for most grazing animals (except sheep, for which flock is mysteriously used), pack for social carnivores (except lions), flock for birds, swarm for insects, and school for fish. There are a few idiosyncratic usages, such as “pod of whales” and “mob of kangaroos,” the latter obviously of fairly recent vintage.
One interesting anomaly is that there is no general term for individuals of domestic cattle. “Cattle” is collective and plural; bull applies to the male, cow to the female, and calf to the young. But there is no term for an individual animal irrespective of gender or age (unlike, say, “horses, a horse, stallion, mare, colt,” “sheep, a sheep, ram, ewe, lamb.”) One farmer I knew used to get around this by calling them “cattle-beasts.”