The spatial variation of the phase director in an unoriented lamellar lyotropic liquid crystal is investigated by H-2 two-dimensional and one-dimensional exchange and PGSE NMR. Exchange NMR probes the single-particle orientational correlation function of D2O molecules that diffuse among regions with different director orientations. The obtained correlation time and the water diffusion coefficient, measured by H-2 PGSE NMR, provide the persistence length of director orientation that is defined as domain size. The nature of spatial variation is revealed by the decay of the H-2 stimulated echo signal recorded with different evolution times. The persistence length of the director is found to be strongly dependent on the rate of cooling the sample from its isotropic phase.