Before starting I want to mention that Lady is the one who helped Dante name his shop "Devil May Cry", which was something she says while trying to comfort Dante over the loss of his brother.
Her original name, Mary, was given to her by her father Arkham, but she chose to renounce that name when he murdered her mother. Dante first calls her "lady" when she refuses to tell him her name, and she accepts it as her real name. Like her father, she has heterochromia. While still a normal human, she is an exceptionally skilled firearms expert and extremely acrobatic in close quarters combat. Her most powerful weapon is the Kalina-Ann, a customized missile launcher similar to a MANPADS named after her mother. In the anime series she works as a solo devil hunter who sometimes calls on Dante for help, and sometimes for the money that he owes her.