Some dynamical aspects of fluorescence and lasing have been studied in a dye-doped cholesteric liquid crystal by measuring the response of the material to nanosecond optical pumping. It has been found that as the pumping energy is increased the fluorescence pulse duration decreases, reaching a minimum at the lasing threshold. Above the threshold the temporal profiles are irregular and consist of a set of narrow pulses whose measured duration is limited by the detector risetime (1 ns). The results are interpreted in terms of a recently proposed model [JETP, 118, 822 (2014)] that makes use of rate equations to account for the laser generation in cholesteric liquid crystals. The prediction of such equations for an experimental configuration appropriate for fluorescence lifetime measurements is analyzed.