No, that's a common misconception. First off, there are lots of types of lung cancers, and smoking is only positively linked to the commonest type - the bronchogenic variety, which makes up about 95% of lung cancers. We'll get to the others later, but for now let us focus on the bronchogenic carcinomas.
The evidence that smoking causes lung cancer is incontrovertible. However, it does not follow that all lung cancers are therefore caused by smoking. (The sun provides light, but not all light is provided by the sun.) Though the figures vary a little from study to study, the data says that the average smoker has a 10-fold increased risk of lung cancer, and a heavy smoker has a 20-fold or greater increased risk.
Of course, buried within this statistic is the fact that non-smokers can also therefore get lung cancers. How? Well, smoking isn't the only carcinogen! Amongst the other factors that have been linked to bronchogenic carcinomas are ionising radiation (e.g. following multiple chest CT scans), asbestos, some air pollutants, an unlucky combination of genes, and even scars.
And then, as I said, that is only the common bronchogenic carcinoma. Other rare lung cancers include bronchial carcinoids, mesenchymal tumours (e.g. fibrosarcomas), and bronchoalveolar carcinomas.
So, while smoking is definitely the number one cause of lung cancer, it certainly isn't necessary to smoke to get a tumour there.