This classic book (just released on Project Gutenberg) is just what it sounds like: Lucy’s dictated history of Joseph’s life. Historians both inside and outside the Church consider it to be a key source. It is especially informative regarding the history of Joseph’s ancestors (chapters 1-9 of 54); his parents, siblings, and childhood (ch. 10-17); and the history of Joseph from the First Vision to the publication of the Book of Mormon and organization of the Church (ch. 18-34). Kirtland and Missouri get most of the balance of the book, with only ch. 52-54 on the whole Nauvoo period.
The most valuable aspect of the book, in my mind, is its discussion of the Smith family and their early inner circle, including the Three Witnesses to the Book of Mormon; Lucy’s descriptions bring them to life in a unique way. Her perspective as a contemporary inside observer of the earliest days of the Church is invaluable, and that’s really the one-phrase reason to read her book.
Readers may wish to be aware that said book has a complex textual history; long story short, Lucy’s dictated memoirs went through several sets of hands and rounds of revision before the 1902 edition (the base for the version on Project Gutenberg) was produced. I thought the 1902 edition was just fine (obviously), but the Joseph Smith Papers project has the earliest manuscript online for all you intense textual critics, and this BYU Studies piece provides some more information on the history of the book and praises a 1996 edition (probably what I’d buy if I wanted a hardcover) based on the original manuscript and edited by Scot and Maurine Proctor, the good folks over at Meridian magazine.