Lucy is the daughter of Connie Abernathy and Blake Abernathy, and can be found working with her family at the Abernathy farm. She has a deceased sister, Mary, who was killed by raiders. She offers to purchase melons from the player character for 3 caps, but passing a speech check brings that amount up to 5 caps.
If you convince Jake Finch to return to his family farm, his mother Abigail can later be heard mentioning Lucy Abernathy as a potential wife for him.
She will tell her father that she wants to join the Minutemen.
During one of the first conversations you have with her, Lucy mentions that she likes having Clarabell around because she is a "free source of fertilizer." This is not just idle chatter, as having a brahmin paired with a feeding trough at any settlement will occasionally add fertilizer to the workbench.