The key here is to work closely with your oncologist with regards to the symptoms your father is experiencing. There can be a few reasons for this. And this include diaphargmatic irritation versus a direct effect on the lung.
Also, it would be good to do either an X-rays or a CT scans of the lung to rule out lung related problems like infection, pneumonitis, or even spread of the cancer to the lung.
When the exact reason for this persistent cough has been defined, then can the doctor prescribe the appropriate treatment for it.