How long can a blod clot in the lung go undetected, and how would you know?

Forever. If the clot is small and peripheral, if may not be detected. That's because they are asymptomatic. Studies show that people have these exact kinds of clots much more often than we are aware.
Shortness of breath. A small blood clot in the lung, usually an embolus, in an otherwise healthy person my go undetected and not cause any symptoms. Most emboli cause chest pain, difficulty in breathing, cough with bloody sputum to sudden death.