Here is my take:
You know your pets, you know if any have a high prey drive or are aggressive. I have found older cats with kittens are generally quite good, they may hiss and run, but they are putting the kitten in it's place and that is OK as long as the kitten is not getting hurt. Very different story if you are putting two adult cats together. Soooooo, what I am saying is: supervise your cat's reaction to the new kitten, if there is no down and out fighting, I would let them be. Hopefully Gibson will be distracted with the little one and will now leave Lucy alone, so all three will be happy
Boy if you saw my house at times when I have foster kittens running all over the house. I have never had an adult attack a kitten, just discipline.
I am sorry I can't comment on your dogs as I don't have experience with dog cat interactions.