Lea is Mab's "trusted enemy." I can't remember which book this originates from, but Harry later says he can be Mab's trusted enemy, like Lea. Mab responds that she won't/can't ever trust Harry. Therefore, it is likely that Lea would try to supplant Mab if she thought she could.
I don't know if it is ever stated explicitly by anyone other than Harry, but it is stated that after Mab found out about Maeve's infection, her voice injured mortals. If this is the case, Mab didn't find out until after Dead Beat.
Lea was probably at the Battle of the Stone Table. Her absence would have been noticed and she did strongly imply that she was going to be there.
I think that she warned Harry away from the Stone Table, and thus becoming the Winter Knight, because she was obligated to as his spiritual director.