While the term mafia wasn't formerly used nor as widespread as when she was alive, Luna does come from a mafia family. Perhaps not in the context that we know today, but historically her family and upbringing bears a striking resemblance to the close-knit, organized crime family units of modern day.
For a little background, she was born in the late 1400s, when the countryside of what would later become Italy was in a state of civil war. City states either bent the knee and submitted to the will of the Vatican and the Holy See, or they rebelled against the Pope. Luna's family, the Montanegras, were among the latter. Not only because they weren't particularly religious, outside of their political connections, but because the Pope at the time was Alexander VI--otherwise known as Rodrigo Borgia, one of the most infamous popes in history.
At the time Luna was born, there wasn't much of the family left. It was just her, her brother, and her grandmother who had taken charge as head of the family. There were no men to stand in her way; her husband had died before her grandchildren were born, and she used her first act as the family head to disown her poor excuse for a son-in-law, throwing him out on the street never to be seen again. She was the donna of the house, and took control of their lands and finances, lessons in which she would later pass onto her granddaughter once she became of age.
Giuliana, Luna's grandmother, adored her, and even named her after herself--Giorgiana. She taught her what it took to survive, and how to protect the family from falling into ruin. She taught her patience, cunning, and above all how to interact with other nobles, and use their weakness to her advantage. Her power was not loud. It was the silence in between, the deep breath before the plunge. Women were often underestimated during her time, and she used that gross misjudgment on their part to pull the rug out from under them.
She built a vast intelligence network to aid her own interests, but that wasn't how the Montanegras amassed their wealth. It was through their armies, and arming them to the teeth. Their main commerce was in the production and selling of weapons, namely swords made from the ore found locally within the mountains. Rifles and firearms were still a fairly new technology at the time, so she had some imported to inspect their quality--which was around the time that her granddaughter became fascinated by them, and took up an interest in hunting for sport.
Giuliana prepared her granddaughter to take her place as head of the family, and taught her what it meant to stand against corruption--even when they were plenty corrupt themselves. She didn't see herself as a hero. Just a woman with an unshakable will, and a bitter disdain for Almighty God and all those who followed in His footsteps.
All things that she passed onto her granddaughter, lessons from the old world that she still carries to this day. Even when she's no longer human: a demon who has been judged and cast into Hell, only to rise again. A mafia heiress with a bone to pick, cold eyes and a gun in her hand.