The Question and Answer section for The Things They Carried is a great resource to ask questions, find answers, and discuss the novel.
O'Brien is commenting how soldiers react in different situations. The quote is a euphemism for stopping crying. Sometimes, especially after battle, soldiers cry.
Curt Lemon was a soldier who got blown apart while talking to Kiley. Lemon's body parts were blown onto a tree. Jensen and O'Brien have to retrieve Lemon's body parts. Jenson starts singing about a "lemon tree". This is ironic because the gravity...
The author was illustrating the way the war itself was volatile... each side making itself known, attacks and counter attacks.