My dad's got lung cancer but was nonsmoker. Could it be genetic / hereditary?

Possibly. Non smokers do get lung cancer, possibly from exposure to other cancer causing agents like radiation, radon, and asbestos. In some cases there is simply no clear cause.
Possibly. The most common cause is tobacco use/cigarrette smoking. This is most strongly associated with squamous and small cell lung cancers. But there are other kinds, like adenocarcinoma that are also common and it is unclear why. Many genetic mutations are aquired and due to smoking, but some may indicate genetic susceptability. More research is needed.
Probable. All cancers have a genetic component. About 10% of the lung cancers occur in non-smokers. To address your unsaid concern, it does not necessarily put you at a higher risk of lung cancer.
Yes. Non or never smokers can develop lung cancer if they have a genetic mutation to such genes as egfr or eml4/alk fusion translocation. Also, patinets with high second hand smoke exposure may develop lung cancer as well.