I'm currently reading The Silk Roads by Peter Frankopan. He has referenced a couple times works that we know existed, but are now lost (I want to say one was Homer's Margites). There is also some speculation that Herodotus wrote a now lost book about the Assyrians. We know of their existence because later authors have referenced it, or the authors themselves have referred to them in other works. I'm curious about what other known authors from antiquity have works that we know existed but have been lost to time.
Too many to list, sadly!
A few notable ones that I would kill to read include:
Greek:
Most of Aeschylus' plays (he wrote many many more, we know for sure, than the 11 that survive).
Plays of Aristophanes: we have 11 of the 40 he wrote, I believe.
Aristotle: many works lost.
Euripides: We have 18 plays. He wrote several times that many
Sappho: we only have a few poems from her body of work.
Sophocles: we have 7 plays. He wrote over 100.
Archimedes' lost books on Polygons and Spheres
Euclid's lost mathematical works, notably the Conics.
Roman:
Numerous lost writings of Caesar's
Most of Livy's history of Rome
Ovid's Medea
There are a couple estimates floating around that we possess something like 0.1% of the body of ancient literature (that is, stuff that was written to be read, not random jotted notes). So really a list of major lost works would be very long, and there wouldn't really be much to say about it (although there are literally books written about books that don't exist anymore). So instead I'll give a couple notes about the source loss from the ancient world.
The first thing to remember is that, all in all, we actually have quite a lot. Sure, it isn't much compared to documents from eighteenth century Europe or anything, but given their 2000 years its is pretty impressive that we have as many as we do. More to the point, we have an even greater number of works that were the sort of works that were really well known. For example, it is often mentioned that there has been a truly dramatic source loss of Greek plays, and this is true from a certain standpoint. But from another, there are three dramatic playwrights that remained enormously famous throughout the entirety of the ancient world: Aeschylus, Euripedes, and Sophocles. There were others, sure, just as there were more Elizabethan playwrights than Shakespeare, Marlowe, and Jonson, but there aren't many people alive today that can name more than those three off the top of their head than them even though anybody can pick up a copy of The Spanish Tragedy by Kyd. This really makes logical sense, it would be far more likely fr the really famous works of a really famous writer to survive than an obscure one.
The other thing to remember is that a lot of ancient works were lost in antiquity. Antiquity lasted a very long time, after all--Augustine was as removed from Cicero as we are from Shakespeare, and more distant from Homer than we are from Charlemagne--and any given work would have a finite number of copies around. Even for some very well known ones, for there is a correspondence between Augustine and Jerome (fifth century) in which Augustine is trying to find titles of works of Varro, the "most learned Roman" of the first century BCE. Thus kind of feeds into the first point: it is quite possible that Cicero had no better chance of getting some of the lost Athenian tragedies than we do.
There is a scene in Carl Sagan's Cosmos in which e goes to the "Library of Alexandria" and says something along the lines of our knowledge of ancient literature being like if we had Shakespeare's Twelfth Night and heard rumors of Hamlet, but the truth is really the opposite--by and large, we have all of the absolute most famous works in antiquity, like Plato's Republic or the Aeneid, and a surprisingly large number of works one down the line. But this only constitutes a minuscule fraction of total works.
That being said, if I could have any known work from antiquity, it would probably be one of the books Hannibal wrote or the travels of Pythias, a Greek explorer. After that, it would be Varro's Antiquities (a history of Rome and Roman culture), the works of the emperor Claudius (particularly his history of the Etruscans), the emperor Trajan's account of the Dacian Wars, or literally anything written by Tacitus.
This is actually a rather common occurrence with ancient sources. In no particular order: the younger Pliny and many other Romans at the time reference the elder Pliny's vast, basically, encyclopedia, though it has been lost. We are missing some books from Tacitus. The geographer Strabo references the work of Eratosthenes but the work of the latter has largely been lost. The Roman historian Ammianus Marcellus wrote a vast history of the Roman empire, but only some of it survives, we know this because he himself references his own work.
The Pelagian Heresy.
Pelagius believed and wrote about his beliefs in the late 4th, early 5th century. He placed a lot of emphasis on the nature of free will, and the belief that Original Sin did not make humans innately sinful. With free will, he believed the Divine did not have as large a role in the influence of doing good works, greatly to the ire of his contemporary Augustine. He was condemned as a heretic, banished from Jerusalem, and he lived out his days in exile in Egypt.
Because of his beliefs, almost all of his writings have been destroyed. Unfortunately some of the greatest surviving excerpts of his writings are in the literature of his opponents, which naturally will not be presented in the truest, most unbiased light.