We investigate the rich physics of photonic molecule lasers using a non-Hermitian dimer model.We show that several interesting features, predicted recently using a rigorous steady-state ab initio laser theory (SALT), can be captured by this toy model. In particular, we demonstrate the central role played by exceptional points (EPs) in both pump-selective lasing and laser self-termination phenomena. Due to its transparent mathematical structure, our model provides a lucid understanding for how different physical parameters (optical loss, modal coupling between microcavities, and pump profiles) affect the lasing action. Interestingly, our analysis also confirms that, for frequency mismatched cavities, operation in the proximity of exceptional points (without actually crossing the square root singularities) can still lead to laser self-termination. We confirm this latter prediction for two coupled slab cavities using scattering matrix analysis and SALT technique. In addition, we employ our model to investigate the pump-controlled lasing action and we show that emission patterns are governed by the locations of exceptional points in the gain space. Finally we extend these results to multicavity photonic molecules, where we found the existence of higher-order EPs and pump-induced localization.