Polariton lasing has recently been observed in strongly coupled crystalline anthracene microcavities. A simple model is developed describing the onset of the nonlinear threshold based on a master equation including the relevant relaxation processes and employing realistic material parameters. The mechanism governing the buildup of the polariton population, namely, bosonic stimulated scattering from the exciton reservoir via a vibronically assisted process, is characterized and its efficiency calculated on the basis of a microscopic theory. The role of polariton-polariton bimolecular quenching is identified and temperature-dependent effects are discussed.