Both the short story "Sonny's Blues" and the poem "Lady Lazarus" are about facing life's despair. In "Sonny's Blues," the despair comes from growing up poor and Black in Harlem. In "Lady Lazarus," it comes from not being able to escape being a woman, which the speaker describes as being used up by men.
The family conflict in "Sonny Blues" is between the uptight narrator, who has managed to climb out of poverty by becoming a teacher, marrying, and having a family, and his musician brother. He is estranged from his brother Sonny, a drug addict who has done prison time. The narrator reaches out to Sonny after his daughter dies in acknowledgment that life's pain is universal. As he gets to know Sonny better, the narrator comes to understand and admire the power of Sonny's music—his "blues"—in helping him to both express and escape the pain of living.
The family conflict in "Lady Lazarus" is between the speaker's desire to die and her family's desire that she stay alive. She has been "saved" from attempted suicide twice, like the biblical Lazarus brought back from the dead. She expresses a wish to once again—as she has done every ten years—attempt suicide. She voices a deep anger and desire for revenge, warning in the last line that she will "eat men like air."
The last line, along with her addressing various "herrs," a word meaning man or mister in German, shows that her anger is directed at the men who have oppressed her. She perceives herself as like a Jew, with the "herr" references pointing to Nazi Germany. She feels used, saying sneeringly:
I am your opus,
I am your valuable,
The pure gold baby.
However, unlike Sonny, this speaker finds no comfort or transcendence in her art. It does not protect her from thoughts of suicide. "Sonny's Blues" is a far more upbeat narrative, told through the eyes of a person who wants to find the thread of good in life. "Lady Lazarus" is told from the point of view of the suffering artist, and it expresses pain and anger, not hope.