Genetic mutations caused by chronic exposure of lung cells to alpha particles from radon gas decay drive cancer formation. As with all cancers, radon-induced lung cancer forms when a genetically compromised cell grows, divides and/or spreads unchecked through the body. The higher the number of genetic mutations thee more likely the chance an individual has of developing cancer.
You can find the full study here: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC546066/