To be honest? Because you are totally misreading the character.
The word lung is, on the left, the radical 肉 meat, flesh, which is used for body parts. You may confuse it with 月, but they are totally different characters. The phonetic on the right is 巿 fú, which is a pictograph of a sort of loincloth, or apron men wore. The horizontal line is the belt, then the part below shows the cloth spreading out along the sides. It went past the knees, so it was used as a cushion for kneeling. It was later written 黻 and 黼.
巿 is four strokes, while market, city 市 is five strokes. They may look similar, but they are different characters entirely.
The lungs look a bit like the apron 巿, which is why 巿 fú became the phonetic element in 肺 feì. P and F are both pronounced with the lips, and F actually entered the language quite late.