Details: Keith was murdered before he even knew of her existence. But it was the spirit of Keith that help Karen carry and give birth to Lily. Throughout her life Lily always thought of her father and enough dreamed of him and questioned his death but overall had a very deep love of him.
Details: Karen fell pregnant very shortly following the death of Lily's father Keith and Karen fell into a deep depression but her pregnancy helped her through it. When Lily was born Karen fell into a coma and dreamed of spending time with Keith and Lily and there he urged her to go back to her daughter. Karen and Lily had a very strong and deep relationship possibly due to Karen being a single parent and raising Lily with the same morals she gave to Lucas (Lily's older brother) and home school Lily and spent all her childhood travelling around the world with her.
Details: Andy was in a relationship with Karen before Lily was born and due to the death of Keith. Years later Karen and Andy recoiled and decided to travel the world together on a yacht and during this time Lily and Andy formed a father-daughter relationship and share the bond of one being extremely close although both admit that they miss Keith/would give anything to have him back.
Details: Lily and Lucas had a very close sibling relationship despite the age gap although their relationship was more like a niece-uncle relationship then brother-sister, but they shared a lot of their feelings. Lily and Lucas didn't regularly see each other for the first seven years of her life as he lived in Tree Hill but then Lucas and his family joined Lily in traveling the world.
Details: Dan and Lily didn't at all have a relationship because Dan murdered her father and because of this Karen wouldn't let Dan see her. But the only time they meet was just are she was born when Dan realized he needed to turn herself in.
Details: Its unlikely that Lily would have a relationship with her grandfather similarly to her older brother because he didn't have a relationship with her father and she travels around the world on a yacht.
Details: Its unlikely that Lily would have a relationship with her grandmother similarly to her older brother because he didn't have a relationship with her father and she travels around the world on a yacht.
Relationship: Great grandfather
Details: Its unknown what type of relationship Lily had with her maternal grandfather because its not known if he is still alive because he's not be mentioned by Karen.
Details: Its unknown what type of relationship Lily had with her maternal grandmother because its not known if she is still alive because she's not be mentioned by Karen.
Details: Lily was born the same day was Nathan's son Jamie and due to the closeness of Haley and Lily's mother Karen it's likely they had a good relationship. But soon after Lily's birth her family went traveling around the world, so its unlikely they saw much of each other - although Jamie and Lily kept in close contact.
Details: Peyton had a good relationship with Lily but due to the age gap it was more of an aunt and niece relationship. Once Peyton married Lucas and started to travel the world with Lily its likely they became even closer.
Details: Lydia was born when Sawyer was two and due to being cousins its likely they would have a good relationship but since Sawyer travels the world with her family its unlikely they often see each over.