Relationship with Victoria
We first see Lord Melbourne in Doll 123. He offers his services as an adviser to Victoria, and at first she refuses. Victoria and Lord Melbourne's relationship becomes strained after Victoria realises he is the only man she would ever want to marry. Lord Melbourne and Victoria eventually part ways after she marries Prince Albert.
At one point we learn that Lord Melbourne was once married and had a son. After his son tragically died, his wife left him and he never saw her again.
Later life & illness
Later in the series Victoria's friend, William, retires to Brocket Hall and works on his garden. After hearing that he is ill, Victoria brings him a toy bird that sings a melody. Following her visit, she goes home and finds her dog dead. During the funeral of Dash, we see Melbourne staring at the bird and the bird looks beaten up.