I think one of the "stories" that teaches Lily most as the central character of this great novel are the stories that Lily assume to be true about Snow Flower and their friendship. Unfortunately, when Lily and Snow Flower return from seeking sanctuary and protection in the mountains, Lily's reputation increases to such an extent that she becomes proud, and is not the true friend that she should have been to Snow Flower. However, when Snow Flower informs Lily that she has found friends in the village and apologises for not being the friend to Lily that she ought, Lily, in her pride, interprets this as a rejection of their special friendship.
It is only when Lily goes to nurse Snow Flower on her deathbed that she realises this was not true, and that she was not "betrayed" by her friend at all, and this was just how Lily misperceived the situation. Lily therefore learns that she was wrong to judge her old friend so quickly, and that she missed out on happy times with her friend because of her pride.