Although lila is the main character of this story we barely ever directly get to know what shes thinking ,why is this?

I'm not sure I really see this in Lila. The author seldom uses direct character presentation, even within the context of first person. I think Anita Desai uses more subtle character development to let us get to know what Lila might be thinking. We see Lila in her words, actions, and reactions to people and situations.