Cats do not really possess nine lives. The origins of the nine-lives myth isn't clear, but many trace the significance of the number of lives and the importance of cats to the ancient Egyptians, who considered cats sacred and worshipped them as gods.
Egyptian folklore states that the sun god, Atum-Ra, came to earth in the form of a cat in order to go down to the underworld and return again. Atum-Ra produced the gods Osiris, Isis, Seth and Nephthys, who are collectively called The Nine.
Also, the number nine carries within it a trinity of trinities. Nine is a mystical number often found in religion and folklore.