It wasn’t lost, and most of it isn’t by Shakespeare. It is a collaborative effort, of which Shakespeare (probably) wrote about a page. If you’re curious, you can easily order a copy.
Since everyone has already mentioned Love’s Labour’s Won, I’d order up the Ur-Hamlet and start copying like crazy.
A couple of ground rule questions before I answer: does the book have to be known to either exist/have existed, or can it be a book that is rumored to have existed/may have existed (Capote’s Answered Prayers for instance, which some say he finished and others dispute, or “show me a missing play from Shakespeare”, etc.)? For that matter, can you request a book that has never existed but should have as in Lucien’s library in The Sandman (“Show me what Mark Twain’s essays on the 2008 Election or the autobiography of Jesus of Nazareth would have read like” for example)?
I think it has to actually exist, but there’s not going to be a penalty for asking for a book that doesn’t. In other words, if you ask for the original, in-Westron copy of the Red Book of Westmarch from which Tolkien translated The Hobbit and Lord of the Rings, you’re going to get a response that no such book exists, so try something else. (And probably remark that you’re a dumbass. :D)
Unless you read Klingon fluently, how on Earth will that be useful to you? You’ll just have to get the English translation, which is also available at Borders.
I would ask for the original, serialized Tale of Genji, organized by date, so I could finally figure out how many chapters and authors the damn thing had.
I’d like to see the Christianity-debunking book Abraham Lincoln wrote when young (and then burned the only manuscript when a friend pointed out what that would mean for his political ambitions).