Lucy's parents met while working in a merchants' guild called "Love & Lucky," eventually striking out on their own when her mother became pregnant. They named Lucy after a quirky accident—the guild's sign was missing a K, so it read "Love & Lucy" instead, and the coincidence stuck with them enough to name their daughter after it.
Growing up on the family estate, Lucy got along well with the household staff and her mother, though she was only around ten years old when her mother passed away on July 7th of X777—the same day the dragons vanished from the world. Her mother was just 29 at the time.
Content compiled by AnimeList.moe from publicly available sources.