The multistage paradigm is widely used in quantitative analyses of radiation-influenced carcinogenesis. Steps such as initiation, promotion and transformation have been investigated in detail. However, progression, a later step during which malignant cells produced in the earlier steps can develop into clinical cancer, has received less attention in computational radiobiology; it has often been approximated deterministically as a fixed, comparatively short, lag time. This approach overlooks important mechanisms in progression, including stochastic extinction, possible radiation effects on tumor growth, immune suppression and angiogenic bottlenecks. Here we analyze tumor progression in background and in radiation-induced lung cancers, emphasizing tumor latent times and the stochastic extinction of malignant lesions. A Monte Carlo cell population dynamics formalism is developed by supplementing the standard two-stage clonal expansion (TSCE) model with a stochastic birth-death model for proliferation of malignant cells. Simulation results for small cell lung cancers and lung adenocarcinomas show that the effects of stochastic malignant cell extinction broaden progression time distributions drastically. We suggest that fully stochastic cancer progression models incorporating malignant cell kinetics, dormancy (a phase in which tumors remain asymptomatic), escape from dormancy, and invasiveness, with radiation able to act directly on each phase, need to be considered for a better assessment of radiation-induced lung cancer risks.