Sure. There's the story of Hester Prynne in 'The Scarlet Letter'. She is a lost woman in the eyes of her Puritan community after being forced to wear the scarlet letter for her adultery. Her soul is banished as she endures public shaming and isolation. Additionally, in some African folktales, there are stories of women who are banished from their villages because they are thought to be witches. These women become lost, their souls banished from the safety and acceptance of their homes, and they must struggle to survive in the wilderness or find a new place to belong.
In the story of 'The Yellow Wallpaper' by Charlotte Perkins Gilman, the narrator can be seen as a lost woman. She is confined and oppressed, which leads to her psychological breakdown. Her soul is banished within the walls of the room where she is kept. Also, in Greek mythology, Medusa was banished and turned into a monster. Before that, she could be considered a lost woman, as she was a victim of Poseidon's advances and Athena's wrath, her soul banished from normal human existence.
One example could be the character of Ophelia in Shakespeare's 'Hamlet'. She is a lost woman who, after being spurned by Hamlet and dealing with the chaos around her, descends into madness. Her soul seems banished as she loses her grip on reality and ultimately meets a tragic end. Another example might be in some Native American stories where a woman who breaks a tribal taboo is shunned and becomes a lost figure, her soul banished from the community's good graces.