If you could rescue one of the many lost books of the Greeks and Romans, which would it be? I think most ordinary walking-around-Americans would nominate the lost second book of Aristotle's Poetics, about which Umberto Eco made such a fuss, and which is presumed to be an philosophical analysis of the genre of comedy.
I myself am not enamored of Aristotle's lit crit. I suspect that if the second book had survived, it would only show that Aristotle had invented a vocabulary to describe various elements of comedy -- and as a result generations of scholars would have felt the need to conduct sterile and inhibiting debates about the precise interpretation of his various technical terms. So therefore, if I were interested in comedy, rather than rescuing the second book I'd prefer to read Homer's lost Margites, famous among the ancients as a comic counterpart to the Iliad and Odyssey. It might have been fun, and we would certainly learn a lot more than we now know about the archaic Greek sense of humor. My suspicion is that we moderns would find the Margites to be a trial, a puzzle, a genuine challenge.
Tragedies also have perished. Anyone who has been dazzled by the great Greek tragedians would want to read the 60 or 70 lost plays of Aeschylus, the hundred or so that have disappeared by Sophocles as well as the 60 or so lost plays of Euripides. No doubt our understanding of the great age of Athens and Athenian religion and art and politics would have to be thoroughly rethought. Nothing more tragic than the loss of the tragedies.
And then there is Livy's history of Rome in 142 books, of which only 35 (plus fragments and reports) survive. How much more full would be our knowledge of the last years of the republic with Livy as a guide.
But if I had to choose one work of the ancients that has perished, I think I would opt for one of the books that were written by Livy's student and friend, the emperor Claudius. Claudius, whose first wife (and one of his better ones) Plautia Urganilla was a native speaker of Etruscan, wrote two books about the Etruscans: a general history, and a volume on the Etruscan language. It's this second book that I would want to rescue. Claudius was the last person known to have been able to read Etruscan, a language which was disappearing in his lifetime.
Etruscan was an isolate -- a language with no known relatives, like Basque. It was written in an early (8th century)variety of Greek, so it can be recited, but it cannot be understood. Etruscan contributed not only its alphabet but a few words to Latin: "atrium," "histrio," "taberna," "stilus," and "cera," for example. Approximately 13,000 Etruscan inscriptions are in existence, mostly on gravestones. There are also about 300 bronze mirrors with religious or mythological scenes on one side, many with Etruscan inscriptions on the backs. They are found in the tombs of women who were apparently literate. There are no surviving Etruscan manuscripts but there is the Zagreb mummy. Sometime around 125 in the last pre-Christian millenium, an Egyptian re-used a linen Etruscan book to wrap a body. Twelve hundred legible words survived. They seem to record prayers and invocations to the gods. Not much else, except for a linguistic mystery in the heart of Europe. Alas that Claudius's books did not make it through the dark age bottleneck!