But there are no a priori reasons for believing that there must have been a 'Latin library'. It's entirely possible that all the works there are Greek. A philosophical library might just possibly produce unknown works of Aristotle - just one of his dialogues, the works that made Aristotle's reputation, would be a sensational find. But the chances of Euripides or Sophocles are slim, I'm afraid. Indeed, it's possible that the new floors of the villa that have been found and not yet properly explored were never part of a library, and will produce no new literature.
It's much more likely that major new discoveries will emerge from the still incompletely studied Oxyrhynchus Papyri. These have produced, as well as the Menander Beard mentions, parts of lost plays by Euripides and Sophocles, poems of Sappho, and the Hellenica Oxyrhynchia. There is undoubtedly more to be found.
Nevertheless, it is fun to play the game Beard does, of naming what one would most like to see come out of the library (though I'm not going to follow her in sticking to Latin works). Of course, the closing of the archive in AD 79 means that it can't possibly include the lost Latin works I'd most like to see, the missing parts of Tacitus' Annals and Histories. We don't have those parts of the Annals that give his account of Caligula's reign, or the beginning of Claudius' or the end of Nero's, and have to fall back on other sources. But what I'd most like is the Histories. We get some of Tacitus' attitude to the emperor Domitian in the Agricola and elsewhere, but it would be marvellous to have his full account of Domitian's reign. I'd also like to see his account of the destruction of Pompeii, since we have two letters that Pliny the Younger wrote to him when asked for research materials, and I'd like to see how Tacitus used those.
One of the comments on Beard's post names the works of the emperor Claudius, and I'd endorse that, particularly the autobiography. I'd also add the autobiography of Augustus (not to be confused with the Res Gestae).
More Greek tragedy would of course be wonderful. I'd particularly like Aeschylus' Myrmidons, at the time better thought of than the plays that now survive. But I'd also like some plays that would give use another complete trilogy - the whole of the Prometheus trilogy would be nice, if only to settle which order they came in. Or perhaps Euripides' Andromeda. This was parodied by Aristophanes in the Thesmophoriazousae - we know this because Aristophanes tells us as much. But only once in all of Aristophanes' parodies of Euripides do we have both parody and object - a burlesque of the Helen in the same Aristophanes play mentioned. Possessing the Andromeda (or the Telephus) would tell us much not only about Euripides, but about Aristophanes as well.
I'd like Theopompus of Chios' lost Hellenica. This would provide new information about the fourth century BC. Plus, it would answer the vexed question of whether he was the author of the Hellenica Oxyrhynchia. The latter work is a fourth-century history, known from two quite significant fragments. It is generally felt that such a significant work can't be by an author that we've never heard of. But all the candidates advanced can be objected to on various grounds - my own preferred choice, Cratippus, I advocate merely because he is the least unlikely. Failing Theopompus, I'd like the title page of the Hellenica Oxyrhynchia, with the author's name on it.
While we're on the subject of fourth century historians, I wouldn't say no to Ctesias' Persica. Like any Greek writing about the Persians, he'd have to be taken with a pinch of salt. But he spent many years at the Persian court, and would be an invaluable source for the later Achaemenid empire.
Finally, I'd like a work in neither Latin or Greek. In his Letters from Pontus 4.13, Ovid reveals that he has written a small book (libellum) in the language of the Getae, the people amongst whom he had been exiled. We might not be able to read it, of course. Indeed, it may not even exist. According to Ovid its contents were praise of the new emperor Tiberius, and his only reason for mentioning of it was to highlight the lengths he would go to, and the depths he would sink to, to praise Caesar, and please can he come home now? So he may have made up the work. But I'd love to have it, and prove that thought wrong.
There's much else as well. Some other tragedians than the Big Three. Any Old Comedy other than Aristophanes. The forensic speeches of Pliny the Younger (post AD 79, but never mind). But before I leave this subject, if you think the loss of creative works like this is something that affects only ancient literature, then talk to some historians of early film or early television. Theda Bara in Cleopatra, or most of the first series of Callan, or much of Doomwatch, are just as gone as Euripides' Palamedes, save that they are better documented, and some of them live on in the memories of those lucky enough to have seen them.