An introduction of nonlamellar-forming lipids into planar bilayers generates packing stress, which is important for the biological functions of plasma membranes and is a driving force for the lamellar-nonlamellar phase transition. We have investigated the phase behavior of a binary system consisting of egg yolk phosphatidylcholine and monoolein (MO) and the changes in the local orientation order of lipids in a lamellar-bicontinuous cubic phase transition. Small-angle X-ray scattering has revealed that the lamellar-bicontinuous cubic phase transition occurs at an MO molar fraction (X-MO) between 0.6 and 0.7. These phases were dispersed to form liposomes and cubosomes to monitor the anisotropy of the incorporated fluorescence probe, in which Pluronic F127, used as a dispersion stabilizer of the cubic phase, has been proven not to alter the cubic structure and the location of the probes. Time-resolved fluorescence anisotropy measurements on these dispersions have revealed that the order parameter of the probe in the lamellar phase increases with increasing X-MO, and that it decreases during the transition to the cubic phase. This observation suggests that packing stress generated by the addition of the nonlamellar-forming lipid is released by the phase transition.