Could right shoulder pain possiby mean lung cancer?

Possibly. Shoulder pain can be caused by a superior sulcus tumor, meaning a cancer that arises high up in the top of the lung. These tumors are uncommon, but can cause severe pain because of pressure on large nerves. There are however, more likely causes for shoulder pain than lung cancer and these should be ruled out first!
Very rarely. Lung cancer can present as shoulder pain. This a rare presentation but in a person with extensive smoking history and no other cause of pain it should be considered if the pain is constant. This type of cancer should be see on chest x-ray.
Anything is possible. There can be many causes of right shoulder pain: including lung cancer, liver disease, gallbladder disease, cervical (neck) disc disease, pinched nerves. However, cervical disc disease and shoulder problems are the most common by far.