Details: Lydia had a very close relationship with her grandson until she died and Jamie was greatly effected by her sudden death. But they were still able to spend time together before she died and they talked about his grandfather. They shared a very close relationship like Lydia shares with all her children. And before she dies Jamie reads are a story his mother would read to him when ever he was ill to help her feel better.
Details: Taylor relationship with her father Jimmy wasn't as positive as the rest of her sisters as Taylor was often seen as the failure of the family in her parents eyes. However, given that Jimmy and Lydia were shown to love all their children equally it is likely that they share the same affection for Taylor as they do for Quinn, Haley and the others but are more unimpressed with the decisions she makes.
Details: Haley's parents are very relaxed and easy going. The youngest of five, Haley's parents were used to children and were their behaviour, especially in high school. However, Haley was different to her sisters, something her father found hard to believe. Both parents took a relaxed approach to parenting informing their child at a young age about sex. When Haley told her parents that she was marrying Nathan, Jimmy was very reluctant. It took the persuasion of his wife Lydia before he eventually grew to like the idea and become a witness at their wedding. After Haley got married, Jimmy and Lydia left Tree Hill with no doubt that Haley could manage life without them. But she was deeply devastated by his death.
Details: Jimmy was at first hesitate to allow Nathan to marry Haley, but when he did he made Nathan promise to protect Haley. Shortly after they were married the James traveled around the world but since Haley was very close to her parents its likely Nathan remained in contact with Jimmy until Jimmy's untimely death
Details: Jimmy first meet Jamie after he was born but it's unknown how much time they spent together before Jimmy died before Jamie was four. When Lydia comes to see Jamie before she dies Jamie tells her he doesn't remember his grandfather very well but Lydia remarks that Jimmy loved Jamie a lot and he has Jimmy's smile.