What character changed throughout the story and how did they change?
The two main characters, Lina and Doon, would have to be considered the ones who grow and change the most throughout "The City of Ember".
Growing up in the underground city, it was their whole world. Life was as life had always been, as far as they were aware. Children grew up, took their assigned jobs, and lived out their lives just as their parents and past generations had done.
When they discover the note that reveals to them, after much work, that there is a way to "escape the city", another step of growth is taken as they contemplate that their known world is not necessarily all there is. This lesson goes even further when they run into the mayor and his helpers who try to stop them from spreading their "harmful ideas."
Finally, when they emerge from underground, they discover that they have been living below the surface of a much larger and glorious world. Sending the note back down wrapped in her baby sister's shirt is their attempt to help the ones left behind to share in their growth.