Kitty seems to me to be very much a natural follower. With Jane and Lizzy all paired off, I can see how Kitty might have turned to Lydia for leadership - I am imagining her as a child of 5, with the headstrong 3 year old being the only one in the house who would play with her.

IIRC, Lydia is 15, Kitty is 17 (for I am two years older!), and Lizzy is 20. I don't think it's ever said, but I'm guessing Jane is 21 or 22, and Mary is probably 19 (maybe 18.) So now I'm trying to imagine this 5 year old little girl trying to form a close bond with her 7(?) year old, very serious sister. I wonder if Mary had decided at that tender age that she must become "accomplished." If so, I can well imagine her chasing young Kitty off so she wouldn't spoil the pages of the books or upset the music stand.

No, I don't think there was a lot of natural affection between Kitty and Lydia. I think they formed a 'pair' by default, rather than inclination. Kitty needed someone to give her direction, to think up what games to play, and Lydia needed a foil and a sidekick.