Clearly these two issues are explored through the central character of Lily and her relationship with her mother, though clearly they are issues that impact a number of other characters as well. Lily throughout the novel struggles with the guilt of having killed her mother and trying to accept responsibility for that. At the same time, Lily's mother showed herself to be subject to a moment of irresponsibility when she ran away without her daughter. As a result fo these two acts, Lily in the novel has to journey towards forgiving herself and forgiving her mother. It is interesting when August gives her her mother's hairbrush with her mother's hair still in it that Lily recognises that in spite of her feelings of hate towards her mother, she cannot dispense with her entirely:
It had grown out of her head and now perched there like a thought she had left behind on the brush. I knew then that no matter how hard you tried, no matter how many jars of honey you threw, no matter how much you thought you could leave your mother behind, she would never disappear from the tender places in you.
We see here that Lily is moving towards acceptance of responsibility and forgiveness in terms of her own act and her mother's act of abandoning her. Lastly, of course Lily is able to achieve forgiveness, both managing to forgive herself and her mother, as she herself comes to realise at the end of the story:
In the photograph by my bed my mother is perpetually smiling at me. I guess I have forgiven us both, although sometimes in the night my dreams will take me back to the sadness, and I have to wake up and forgive us again.
The novel thus points towards forgiveness and responsibility as being part of the journey of life. It is interesting that this quote indicates that forgiveness is something that needs to be re-enacted again and again, indicating the continual struggles of emotions and feelings that need to be resolved.
It is explored through the realization of her guilt of killing her mother, and even in her dreams, dreamt about going up to the heaven above and meeting with her beloved mother to ask for her sincere forgiveness, but she has little doubt that her mother would kiss and forget about the whole big matter.
Later on in the novel, she was angry with her mother's abandonment of her and going to another family, giving birth to August, which was her friend, angry with her leaving her behind lonely and cold, wallowing in her victimhood and didn't want to forgive her. She thought that her mother was responsible for her plight now and got so worked up that she thrown jars of honey at the wall to let up steam.
This two excerpts from the book shows two contradictions between the themes of responsibility and forgiving. At one part, she felt guilty and responsible for the death of her mother, but then in another part, she felt that her mother was partly responsible for her plight and didn't wanted to forgive her from abandoning her with her husband.
At the same time, Lily ponders over forgiving her mother and being angry for her mother for abandoning her, making her life miserable and lonely. She also thought deeply why is so difficult and impossible to forgive someone for her past wrong actions and deeds
There are many parts of the novel that talk about these issues, perhaps the most poignant example is the relationship between Lily and her (dead) Mother. You can find all of those issues in the last two chapters, when Lily learns more about her mother and her real problems, and at last she learns to forgive her.
Another example would be Lily and her father. Her father has the responsibility to raise her, but he also has issues with forgiveness, especially when it comes to forgiving his wife.