I am fairly certain the youngest man is Lorenzo. That much I assume is a given. But the portrait of Vitale (Number 2 in the picture) is where I start to get confused. Vitale's hair is completely grey in his portrait. So either the man in the portrait is a leftover of an early Vitale design or Vitale's father.
This would make me assume that when Lorenzo was young he and his three older friends formed the mob and somehow Lorenzo became the leader.
The man with the glasses and sweet sideburns is most likely Filia's father. It is stated in Squigly's story mode that Fillia is decended from a mafia member and he seems like a likely candidate. First off because he is least scummy looking and secondly because his wife looks a bit like an older Filia (especially when you consider that Filia was blond prior to being infected with a parasite.) I also like to theorize that this blond woman is related to Lorenzo, who was also blond in his youth. Perhaps she's his sister or daughter. Making Lorenzo either Filia's uncle or grandfather.
The fourth man looks especially evil. His design is quite reminiscent of Irvin. I find Irvin intriguing because he only appears very briefly with no explanation. When candidates for DLC were announced he wasn't even nominated. This is really strange when you consider that Minette (who cannot fight) and Andy Anvil (who is primarily just one of Peacocks sidekicks) were nominated. So I think it is safe to assume that Alex Ahad has some plans for Irvin, perhaps having something to do with his role investigating the Medici Mafia. If that man in the portrait is a relative of Irvin's then maybe that would shed some light on his true intentions.
So there you have it, my paranoid ramblings on four portraits in the background of a stage in a fighting game. But then again, Alex Ahad had been writing the Skullgirls story/universe for many many years. Skullgirls has a deeper lore than most other video games but much of it isn't given a chance to be shown within the game itself. Sometimes I wish Skullgirls was an RPG, just so I could explore the world.