This is a list of three names of freedmen (former slaves that were released by their master).
Roman male names for free citizens in classical time usually consisted of three parts (known as tria nomina): Praenomen, Nomen gentile, Cognomen.
- (Praenomen) Marcus (Nomen gentile) Tullius (Cognomen) Cicero
- (Praenomen) Gaius (Nomen gentile) Julius (Cognomen) Caesar.
Without going into detail about how these names functioned, the first part, the praenomen, was picked from a very small list. In classical times there were only 18 known praenomina, and most of these were rare. More than half of all Romans (as far as we know) were named Marcus, Lucius or Gaius. Add Publius and Quintus, and you've got three quarters of the male population! Because this was so, the praenomen was generally abbreviated. There was a standard set of abbreviations that was very consistently adhered to. You can find a nice list of Roman praenomina, including known abbreviations, on Wikipedia.
This is how we know the first L stands for Lucius.
Slaves had only a single name, which was often Greek (whether the slave was from Greece or not).
Now when a slave was freed, he received a full name befitting a free man. Generally speaking, he adopted the praenomen and nomen gentile of his former master, and used his former slave name as his cognomen. So, when (say) one L. Valerius Flaccus released his slave Baricha, the newly minted freedman would now be named L. Valerius Baricha. But lest anybody forget that he was a freedman, the term Luci libertus (freedman of Lucius) was inserted before his cognomen. Since this was very formulaic—the usually abbreviated praenomen always followed by the same word libertus—it was generally abbreviated. So you had L. L. for Luci libertus, M. L. for Marci libertus, etc. So his full name was: L. Valerius L. L. Baricha.
Note that this addition was and is often left out. I believe it is typical for (funerary) inscriptions, and it is in the same place where (in the case of free-born citizens) one would find a similar reference to the father: L. Valerius L. f. Flaccus = Lucius Valerius Luci filius Flaccus = Lucius Valerius, son of Lucius, Flaccus.
For freedwomen, it worked similarly, except they had no praenomina (and the second L stands for liberta, of course).
Find here a nice explanation (with exercises!) of freedman/freedwoman names from Oxford University's Ashmolean Museum.