Roman patricians, who as noblemen were the sorts of people likely to have their name inscribed in stone so people centuries later might actually know what it was, had a surprisingly small number of first names (less than 20 by the 1st century BC), which were known as praenomina, or "forenames."
The most common of all of the praenomina was Lucius, a name almost certainly derived from the Latin word lux (gen. lucis), meaning "light," just edging out Gaius, and handily beating Marcus.
In his 4th or 5th century epitome De Praenominibus ("Concerning the Praenomina"), Julius Paris claims that the name Lucius was given to children who were born at dawn, although the vast numbers of people named Lucius in Roman times suggests that this criterion was not strictly observed. We literally know of thousands of men named Lucius just from late Republic and early Imperial times alone.
Along with Marcus, Lucius is one of only two Roman praenomina to have survived unaltered into modern times as a name in widespread use.