The irony of Lily's parents
As spoiled white hippies, Lily's parents represent what she is not. She does not identify with privilege, because it was stripped away from her and she was given a hard life instead. She does not identify as white, because although her skin is white, her cultural identity is firmly Muslim. They are also ironic because they mistreated her and then died.
The irony of a foreign orphan
By becoming orphaned, Lily accidentally finds herself alone, trapped in a foreign land where nothing makes sense. She is used to travel, but she has never been trapped long enough to realize that people live completely differently in different parts of the world. But, ironically, this foreign orphan is in a good place to be orphaned, because a recent Muslim convert adopts her, and the Sufi mystics at their temple are welcoming to her.
The irony of religion and prejudice
Although religion is necessarily about the unknown (Where did we come from? Why are we here? What is the nature of reality?—questions like these), there is also an direct relationship between religious dogma and prejudice. Because dogmatic thinking can be done in the guise of religion, there are those in Lily's community who mistreat her, basically because they are racists against her. Aziz helps her understand that as a black man.
The irony of revolution
To revolt against the government is ironic, because the government is allegedly a useful feature of society. The people who want to overthrow the Ethiopian government do not believe they are causing conflict for conflict's sake; they think they are fighting for something else, like a new kind of order, but in Lily's life, it is completely evident that violence did not solve any problems whatsoever.
The irony of community
In the West, Lily sees that community is done differently. There are still communities, but it is regarded as heinous and strange when she confronts the public who live in her apartment complex. People simply don't understand her motivation, but her motivation is to be known by a community. In a way, she is like a religious martyr of loneliness, alone in her family, alone in her communities, and alone from Aziz.