Approximately seven millennia ago, primitive peoples were using the holophrase pleu in the context of "to flow" or "to float". Since these Proto-Indo-European speakers somehow figured out that lungs float while other body parts do not, pleu was conjugated into the word pleumon, which meant "lung". This went into Greek as pneumon, which was later altered into pneumonia to describe "an inflammation of the lungs". Meanwhile, this pneumon became the Latin word pulmo, also meaning "lungs". This became pulmonarius, or "of the lungs". Through French, this then jumped the English Channel into English scientific jargon, where it took the form of pulmonary, a word which remains today (defined as "relating to the lungs") and precedes a laundry list of respiratory diseases. In retrospect, it's not that surprising to see these two words connect, but it's interesting to observe how they develop over time.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.