We are told that after Jane and Lizzy are married, Kitty spends most of her time with them, which means that at some point she is likely to be at Pemberley when Georgiana is there. And we are also told that Kitty improved as a result. I'd like to think some of that might have to do with Georgiana's example. Just speculation, but since JA afterward said that Kitty would be married to a clergyman near Pemberley, she must have spent a good deal of time there!