Poor Livvy, poor Kelly!!!
Another suggestion is to try to keep Noah seperated at times, because actually he is the source of the problems...so Livvy would have the chance to peacefully interact with the other cats and gain more trust...

I hope you'll find a way to help them to coexist peacefully again...I think the most important thing now is that the others don't jump in and join Noah attacking that poor girl...

I keep you in my thoughts!!!
Paws and fingers crossed!!!

P.S. Even when I'm breaking a few nerves with my constant book suggestions, but please read
Wright, "Is my cat crazy?"
Dodman, "The cat who cried for help"
Cats are so sensitive and it's good to learn more about their behaviour ...