The letters themselves are Graves's invention, but they incorporate phrases from the classical sources, which he weaves skilfully into his own fictional account.
For example, the phrase about the Roman people being at the mercy of "such slow-grinding jaws" is attributed by Suetonius to Augustus, speaking of Tiberius.
Once again, prophecy provides a link between what we as readers may know, and what Claudius could not yet know by any other means.
Here, Livia tells Claudius that Thrasyllus, an astrologer at the court of Tiberius (mentioned by both Tacitus and Suetonius), has predicted that Caligula will be murdered and that he (Claudius) will be the man to avenge his death.
This prophecy by Thrasyllus (an invention by Graves) is Delphic. Livia assumes that the prophecy relates to herself (that she will become the greatest Deity the world has ever known) whereas we can see, with the benefit of hindsight, that it relates to Jesus Christ.
This is a rare anachronism on Graves's part. The fear that he attributes to Livia is not a fear that a First Century pagan Roman would have entertained. The Hell that she fears is that of Dante, not Virgil.
Interestingly, Claudius does not ask Livia about the death of his fiancée, Livia Medullina Camilla. It is also interesting that, if we believe Claudius's account of this conversation with Livia, we must assume her (that is, the fictional character, not the historical one) to have been guilty of most of the murders that he suspected her of. The question for the reader is: do we trust Claudius at this point, given what we know about his background, and his feelings about his grandmother? He goes on to say that "it all seemed like a drunken dream." Perhaps it was?
This story of the unfortunate fisherman is based on an account in Suetonius's The Twelve Caesars, and is just one example among many of Tiberius's arbitrary cruelty during his period on Capri. As with the stories of his sexual depravity, it is impossible to know how much truth there is in such claims.