The Happy Isles of Oceania by Paul Theroux (1992). Theroux paddled a collapsible kayak around the Pacific islands, including Hawaii, and wrote about what he found with his characteristic mix of literary curiosity and unsentimental observation. The Hawaii section captures something of the tension between the islands' natural grandeur and their complex modern reality. Not a guidebook — closer to a meditation on remoteness and belonging — but it puts Lanai and the Hawaiian chain in a useful frame before you arrive.
Hawaii by James Michener (1959). Michener's sweeping historical novel follows Hawaii from its volcanic origins through the waves of Polynesian settlers, New England missionaries, Chinese and Japanese immigrants, and haole landowners who shaped the islands into what they are today. The Dole pineapple era and the plantation economy that built Lanai City are woven into this history. At nearly 1,000 pages it is a serious commitment, but readers who finish it arrive in Hawaii with a much richer sense of why the place looks and feels the way it does.
The Pineapple Story: Dole and the Making of Hawaii — various histories of the Dole Company and Hawaiian plantation agriculture trace the same arc visible in Lanai City's wooden cottages and fading company buildings. Sanford Dole's transformation of Lanai from scrubland into the world's largest pineapple plantation, and its subsequent collapse by the early 1990s, is one of the more instructive chapters in American agricultural history. Any library copy of a serious Hawaiian history — Ronald Takaki's Pau Hana: Plantation Life and Labor in Hawaii is one of the best — will give this context in depth.