Lianne is shown to be obsessed about death, but in a different form from that which occupies her husband's mind. Following the suicide of her father and the way in which Alzheimer's patients face an incredibly slow and cruel death, 9/11 focuses her even more on death. Lianne is shown to be desperate to cling on to life as she fears her own death, and in particular a slow death through Alzheimer's or a depression that might lead her to imitate her father's suicide.
However, after the disaster, we can see that Lianne slowly moves away from this fear. She continues to try and understand death and in particular 9/11 through editing books abotu terrorism, and she struggles to try and maintain and protect a sense of order in her life. Seeing a performance of the Falling Man shakes her composure, and later, when she hears of this actor's death, she concludes that she was never able to understand his actions.
Lastly, what brings Lianne past this troubling period in her life, and gives her the courage to leave Keith, is her embracing of religion and her desire to engage with life. Keith senses this and expresses his reaction to it in the following way:
She wanted to be safe in the world and he did not.
Lianne's embracing of religion and her desire to be a family therefore express her conquering of her fear and uncertainty about life and death. At the end of the story, she, unlike Kevin, is shown to have moved on and to be ready to live life to its full once more.