I must admit that my interest in this subject has sort of waned for a few months, but it may wax again!
Does Lightfoot's treatise need any rebuttal?
If Jerome and Augustine thought the letters were genuine, I trust them more. They were closer, they were fluent in Latin, they probably knew something of how the letters came to light.
Why is there no record of the correspondence for 300 years? Presumably the letters were held by the descendants of Seneca's family and then brought forth after Constantine, when it was safe to publish them. Alternatively, the descendants of Seneca may still have had strong connections with the Roman senate, which was at the time of Jerome in danger of being closed down by forces in the church (nicht wahr?). The letters could have been brought forth for a political purpose. But who knows; the fourth century isn't my area of expertise.
Lightfoot seems to think that these letters would be of little historical interest. I just read a book by Goodspeed who thinks that the combined corpus of Paul's letters had a tremendous influence on much of the New Testament, including the letters of Peter and John and the Revelation. Goodspeed thinks the letters were collected sometime around 80 or 90 AD (I don't remember exactly). If the Paul-Seneca correspondence is genuine, then they may have been collected (saved) by Paul himself and shown to Seneca, as early as 60-65 AD.
As for the content of the Paul-Seneca letters--they are personal correspondence! We should not expect them to be like the other writings of the two men. It is possible that they wrote elliptically, knowing that in Nero's regime there were spies everywhere.
Perhaps I will add more later. Write me if you want.
