How long could someone live with a punctured lung before getting to the hospital?

Depends on size. Pneumothorax is when air escapes from the lung via a hole in the lung such that air accumulates in the chest cavity and causes the lung to collapse. A small leak will result in a small pneumothorax and may be asymptomatic. A large leak could result in a massive pneumothorax and be very dangerous even fatal.
Go to ER NOW! If you are worried about a punctured lung, you should go to the hospital now. This is a medical emergency and requires hospitalization for repair. It can be a life-threatening emergency.