Lucy was born in Arefu in 2252. At age 25, she struck out on her own and headed for the "big city," leaving the small settlement of Arefu and finding her way to Megaton, where she currently resides. Even though Lucy is far from home, she misses her folks and her younger brother, Ian West. She frequently communicates with them via letters she sends there, but as of late they haven't replied, and she fears that either they are in trouble, or the letters simply aren't getting through.
If the Lone Wanderer speaks to her after visiting Arefu but before finding her brother, they can inform her what happened to her parents, and she will ask the player character to find him for her. If one completes the Blood Ties quest one no longer has the ability to inform her about what happened to her family.
She seems to have an attraction to the player character, as after finishing dialogue with her she requests the Lone Wanderer see her when visiting Megaton.
During the Blood Ties quest, one can extort 100 caps from Lucy after discovering the fate of her parents in Arefu. The player character must have the Scoundrel perk in order for this check to appear.
The following is based on unverified behind the scenes information and is speculative and may not be accurate.
Lucy's name is a possible reference to the character Lucy Westenra from Bram Stoker's Dracula. They both have connections to vampires, and they were the first victims of a chain of unfortunate events that affect their loved ones.
End of information based on unverified behind the scenes information.