One of the best examples of irony in Act II is when George Murchison calls Walter, Prometheus. Walter never understands the illusion but those in the audience probably do. Prometheus was a Greek Titan who, contrary to the wishes of Zeus, brought fire to humans from Mt. Olympus. This was in order to help humans stay warm. Ironically, Walter wants to bring liquor to humanity which is not very helpful.
In order to punish Prometheus, the gods had him chained to a rock and had an eagle eat his liver each day. At night, the liver would grow back and the process would start all over again. George's implication is also that Walter is destroying his liver because he drinks too much. Walter does not understand the irony of this either and thinks George just made up the name.
Before Joseph Asagai, a Nigerian student, visits the Youngers' apartment, Beneatha warns her mother not to say anything about African culture in front of Joseph. Although Lena Younger has good intentions, she has little knowledge about her African roots and is ignorant about foreign cultures. Beneatha even corrects her mother when she confuses Nigeria with Liberia and mentions to Lena that Africans need more salvation from the British and French. When Joseph Asagai arrives, Lena reiterates Beneatha's arguments about Africa to Joseph and ironically comes across as a person familiar with her African roots. It is ironic that Joseph Asagai views Lena as an enlightened person that is familiar with her African roots. In reality, Lena is ignorant about African culture.
It is ironic that Asagai is the only one to truly understand the American Dream, and he is foreign.