It seems you might be thinking of the Pulitzer Prize for "To Kill a Mockingbird", which she won in 1961. This award was for the novel, not an audiobook adaptation.
While there are audiobooks of "To Kill a Mockingbird", Harper Lee herself was not involved in their creation. She passed away in 2016.
The Quill Awards are a prestigious award for audiobooks, but they are not awarded to authors directly. They are awarded to audiobook publishers and producers for their work.