Siamese Lynxes have a chance to be spawned when digging up a Griffin Burrow with an Ancestral Spade while the Mythological Ritual is active and the player has a COMMON or higher Griffin Pet equipped. A Mythological Creature also has a 0.4% chance to spawn when a Mob is killed. The stats and spawn chance of the Siamese Lynxes are dependent on the rarity of the player's Griffin Pet.
The Siamese Lynxes will walk towards the player and attempt to attack them. Only one Siamese Lynx can be hit at a time, which is shown with angry villager particles. After one Siamese Lynx is hit, the particles will appear over the other one. If one Siamese Lynx is killed, the other will always be able to be hit.
Azrael is likely based on the cat in The Smurfs. It inherits also its name directly from the Islamic and Jewish traditions of Azrael, the Angel of Death.
Bagheera is most likely based on Bagheera the black panther in The Jungle Book.
One of the cats is internally named Siamese Cat in vanilla Minecraft.
As all other mobs, they can be Runic, either one or both of them.
Ancestral Spade while the Mythological Ritual is active and the player has a COMMON or higher 
Griffin Pet equipped. A Mythological Creature also has a 0.4% chance to spawn when a Mob is killed. The stats and spawn chance of the Siamese Lynxes are dependent on the rarity of the player's Griffin Pet.
Ancient Claw
Coins
Combat XP
Experience Orbs
Enchanted Gold
Antique Remedies
Crochet Tiger Plushie
Dwarf Turtle Shelmet
Tasty Cat Food in order to create 
Pre-Digestion Fish.
Voodoo Dolls, due to it being a Pufferfish.
Added Siamese Lynxes.