Following experimental realizations of room temperature polariton lasing with organic molecules, we present a microscopic model that allows us to explore the crossover from weak to strong matter-light coupling. We consider a nonequilibrium Dicke-Holstein model, including both strong coupling to vibrational modes and strong matter-light coupling, providing the phase diagram of this model in the thermodynamic limit. We discuss the mechanism of polariton lasing, uncovering a process of self-tuning, and identify the relation and distinction between regular dye lasers and organic polariton lasers.