Lily Grace Richards and her family is known for a clothing company, Richards Clothing, that also does a lot of business for Funtom (Ciels company). Lily met Ciel when they were young, so before the fire. They used to see each other a lot as Ciel was Lily's best friend as a child. When Ciel wasn't with Elizabeth, he was hanging out with Lily during the day. Well, rumor had it that Lily used to sneak out of her manor at night and ride her horse over to Ciel's manor. (Ciel was 10 according to a timeline so that would make Lily about 9.) Rachel and Vincent expected her most nights, even if she didn't come.
The night of the fire, Ciel and Lily had already planned their "sleepovers" as it was Ciels birthday. Lily rode over like normal. She went to the garden and made a flower crown like usual. Well, while doing so she smelt smoke. She looked up, seeing the manor begin to burn. She didn't know what to do. However, she stood up and her dress was caught in the thorns. So, after to struggling to free herself, the manor was now fully engulfed. She could see Ciel exit. Of course, she was relieved. However, she believed she saw him run back inside (it is later found out that it was one of Ciels kidnappers that had run inside.) well, lily went after "Ciel." She looked as much as she could but she knew she had to get out. After some struggle, she got to the exit. However, as she was coughing from the smoke, a beam fell before her. To cover her face, she used her arms. They were badly burned and as she grew up they healed, but left very noticeable scars.
When Ciel returned, she vowed to herself to never let him see the scars. She would never physically speak to him again. She still writes letters, but always makes up some excuse as to why they can't visit each other.