How do you think Harper Lee felt when she was writing To Kill A Mockingbird?

She was most probably thinking about how best to do justice to her own experiences of growing up in Alabama during the 1930s, as well as using her background to make general points that would resonate with people who hadn't shared those experiences. To Kill a Mockingbird is a heavily autobiographical work, and so, in writing the book, Harper Lee will have wanted to share some of her life experiences—especially with those who wouldn't have seen or encountered the kind of things that she had.
Doubtless it must have been very important for her to present as truthful an account as possible of what life in a small Southern town was like in those days. This was her world, after all, a world with its own unique rhythms, traditions, and conventions. It's against the background of small-town Southern life that Harper Lee set out to explore more universal themes.
Of course we cannot be absolutely sure as to what Harper Lee felt when she was writing To Kill a Mockingbird, but it seems a fair assumption that she wanted to deal with both the particular (the details of Southern life) and the general (broad themes such as growing-up, racial intolerance and empathy).