What's your personal statement on the book Lyddie? What did it mean to you? Can you relate or connect to the book and/or its characters?
This question is entirely up to you. In order to best answer the question though, a complete reading of the book is necessary. Reading chapter summaries and character descriptions won't give you the full impact of having read the entire book.
When a teacher asks "what did it mean to you," the teacher shouldn't mind if you say that you liked it or didn't like it. What matters to the teacher is that you state an opinion and then clearly explain yourself with multiple explanations. Using quotes and direct textual evidence from the book always helps too.
Even if you hated Lyddie as a book, I doubt it left you completely void of meaning. At the very least, a reader learns more intimately what it was like to be a factory girl and work in those difficult conditions. People complain about their harsh work environment and difficult bosses now, but it was nothing compared to what Lyddie had to endure. Especially considering how young she was. Students read history texts all of the time that mention harsh conditions for certain time periods and places, but Lyddie helps make those thing more real to readers. That's what I would focus your personal statement on.
Personally, I can relate to Lyddie as a character. I'm not a girl, but I did work in a factory, on an assembly line for a portion of my life. It was terrible, and it gave me motivation to stay in school. Lyddie enjoyed working the mills and earning money, but at the end of the story, she chose to go to college and further her education. There are other characters that you might be able to relate to, but Lyddie so centrally dominates the text that it is tough to get a deep look at other characters.