Lucy was born in Arefu in 2252. She moved away from her family to Megaton and lives alone in her rather spacious home. She spends the majority of her time sitting at a table in Moriarty's Saloon. Moriarty tells the player that Lucy is scared of something, but he doesn't know what.
If you kill Evan King, she will refuse to engage in conversation with you.
If you talk to her after visiting Arefu but before finding her brother, you can inform her what happened to her parents, and she will ask you to find him for her. If you complete the Blood Ties quest you no longer have the ability to inform her on what's happened with her family.
She seems to have an attraction to the player character, as after finishing dialogue with her she requests the player see her when visiting Megaton.
During the Blood Ties quest, the player can extort 100 caps from Lucy after discovering the fate of her parents in Arefu. You must have the Scoundrel perk in order for this check to appear.
"I heard about your little killing spree in Arefu. Get the hell away from me!"