Is having pain in the lung typical of copd?

No: Pain in COPD is uncommon. Only the lining of the lungs has nerve endings so pleurisy (an inflammation of the lining) is painful but lung disease itself is not.

No: The lungs have no pain fibers and so don't send pain signals to the brain. The pleural surfaces lining the chest wall are exquisitely pain sensitive and cause the sharp pain we call pleurisy, but this is not typical of copd. Cough is the typical symptom of nerve irritation in the lungs.

Depends...: The lungs themselves do not have the ability to hurt but cough, a common symptom of copd, can lead to musculoskeletal chest discomfort that can be quite painful. There are also painful complications of copd, like a collapsed lung. So, it depends on the type of pain you are referring to.