"The Day Lady Died" has to be one of the most unusual elegies (a poem written mourning a deceased person) in modern poetry. The title couldn't be any clearer: this poem is about a person who has died. But in the poem itself – silence, at least until the end. What do going to the bank and buying books have to do with Billie Holiday or her death? O'Hara assumes that we already know who "Lady Day" is, that we love her music, and that we care about her death. From the reader's perspective, it's a bold move, but we think it works masterfully.
The poem leaves open the possibility that the speaker just isn't that distressed by Holiday's death.