"The Day Lady Died" is a recounting of a day's events. The first thing I noticed was the very sparse punctuation and that the entire poem is one run-on sentence. I scrolled back up to the top and I read the title again. "The Day Lady Died." It then hit me that this poem does not mention whom "Lady" is (although I was later informed she is Billie Holiday). "It is 12:20 in New York a Friday/three days after Bastille day, yes/it is 1959 and I go get a shoeshine/because I will get off the 4:19 in Easthampton/at 7:15 and then go straight to dinner/and I don't know the people who will feed me (lines 1-6)." Where is the mourning of this lost "Lady" that the title implies? He cared enough to write a poem about her but where is she in it? When he finally learns of her death, he is overcome with a flashback of hearing "Lady" singing in a bathroom. That's all he mentions of her. He doesn't mention being stricken with sadness, only remembrance. That's just it: life goes on without her. Everyone mourns in their own way and he's deciding to honor her with a beautiful memory of her voice.
There is also never a period in the poem. Periods are used to mark the end of something and which in a sense, makes this poem never ending. He'll have to go on forever without "Lady" but she still exists in his memories and will forever exist in this poem.