It doesn't matter what you lore.
However, the fastest gain method I've found was just to vet and tame as much as possible. You really don't need to focus on lore for it to train, as it'll gain much faster than your other skills. If you want, spar a couple of pets with each other and vet them. I let my kitsune spar for a while to get some vet/lore gains, and they gained from it too.
Wenchy