Animal Lore raises passively along with Taming and Veterinary. Skill gain from direct use has been limited with the implementation of publish 16 since you can only successfully use it on tamed creatures (your own as well as other peoples') until you reach 100.0 skill.

The most effective way to gain is by letting it raise during your Veterinary practice.

While applying bandages to your pet, watch out for a passive animal lore gain. As soon as it occurs, lock your Veterinary skill, stay in the spot and keep applying bandages. Eventually you will stop gaining, then unlock your Veterinary skill, change location and keep practicing. Movement seems to influence your skill gain positively.

If you follow this advice, you will raise both your Veterinary and Animal Lore skills quickly and efficiently, even beyond Grandmaster level.