When Joe first meets Lucy, she tells him that her father is Gaius Sallustius Lucullus. If you ever look him up, you'll find him referred to as Sallustius Lucullus (because so many people had 'Gaius' as their praenomen, it was usually dropped). In the book, he is known only by his cognomen Lucullus. If this seems baffling, you might like to read the page about Roman names, here! It IS pretty confusing!
Lucullus did exist, and as in the book, he was the Governor of Roman Britain late in the 1st century AD. We don't know very much about him, and we know nothing about his family, so they all came out of my imagination!
The one thing that does seem fairly certain is that he was put to death by the emperor, Domitian, in around AD89. The person who recorded this fact stated that Lucullus had named a new lance after himself which made the emperor angry. Whether this was true, or whether there was another reason, nobody knows.
One of the big things we don't know for certain is whether he was the owner of Fishbourne Roman Palace. There are lots of theories about who the palace was built for, and whoever it was must have been pretty important. A historian called Dr. Miles Russell makes a very convincing argument for Lucullus as the owner of the palace in his book, "Roman Sussex", (which Joe reads in my book!) but if you go to Fishbourne, you are likely to hear that the palace was built for a King Cogidubnus.
A model of Fishbourne Roman Palace as it may have looked in Lucy's time, to be found in the museum there. Not a bad pad!
This is the problem with such ancient history: nobody knows very much for certain!