Unless the cat is sick and one does not know how to do this, this may kill a cat and not necessarily give them longevity let alone "eternal life".
Writting speculation and saying at every line it was the Gods is not a good thing. A lot of things can be possible, but the details are not always the same.
The Gods could likely make immortal animals but this would be with genetic engineering. The slightest energetical disturbances can kill animals very easily or mess them up let alone passing them so called "Risen energy".
Even with light and breathing energy into them, requires care. Their souls are not like humans.
The souls of animals are sensitive and have another type of destiny. Feeling like an animal has to live forever is mainly due to emotional fear of human deprivation and not all that much about the pet itself.
I truly hate when a familiar dies, worst feeling ever, but they do return and get reincarnated to us. The reincarnation process allows also for further re-training, removal of mental scars from the animal, and more.
HPS Shannon said:
I was told that one can extend the life span of an animal by directing, programming and extending one's own life force to them when one is risen, and then work on making an animal immortal after one completes the magnum opus.
I plan to do this for my beloved pet cat, whom I love so very much.