Gordon, you have three sudden and premature deaths here: Roosevelt, Leon Trotsky and Lenin - three men who left their mark in history, struck down by an assassin or a stroke (which is also an assassin). When they died, a bright light, for good or evil, went out in the world.
"Pen in hand" and "in his shirtsleeves"are images of work. Their sudden death truncated their great work while they were still at it.
"In one's shirtsleeves" is an idiom which means "wearing a shirt with nothing over it". In the generation that the novel is set, men normally wear a jacket over their shirt - Lenin was nearly always photographed in a three-piece suit, even when he was addressing a crowd in the streets. "In his shirtsleeves" is an image of Lenin working without his jacket on.
As to why the passage says "the nation's purpose in its shirtsleeves", please see my explanation above.
Gordon, you are reading a novel with rich historical detail, written with great literary skill. It encourages you to get to know 20th century history of the world, too. This is particularly interesting for someone in your situation, where the study of history is a politically sensitive and controversial matter.