The radiative decay rate of a fluorescent probe in an optically thin layer is known to depend on the orientation of the probe and on the refractive indices inside and outside the layer (W. Lukosz, Phys. Rev. B 22 (1980) 3030). Fluorescent probes in phospholipid bilayer membranes approximate such a system. The natural lifetime is expected to vary with the refractive index of the medium surrounding the bilayer. The lifetime variation with the refractive index depends on the orientation of the fluorescent probe. This can be used to retrieve the second-rank orientational order parameter, <P2>. The fluorescence decay of all-trans 1,6-diphenyl-1,3,5-hexatriene in L-alpha-dipalmitoyl-phosphatidylcholine large unilamellar vesicles (LUVs) was measured at a temperature well below that of the phase transition. The refractive index of the medium was varied by addition of glycerol or sucrose. The observed change of decay time with the refractive index followed the theoretical prediction. The value of the order parameter, <P2>, recovered is significantly lower than that obtained from fluorescence polarization data. Possible reasons for this disagreement are discussed.