Dynamics of nano-sized colloidal particles dispersed in a dilute lyotropic lamellar phase of a nonionic surfactant has been studied experimentally by ac electrophoretic light scattering and direct tracking under a microscope. The obtained frequency spectrum of complex electrophoretic mobility shows two relaxation processes at about 1 kHz (HF relaxation) and a few Hz (LF relaxation). These relaxations are due to the hindrance of free diffusion of particles by the hierarchical local static and dynamical structures of lamellar phase. From the direct tracking of fluorescent-labeled particles under a microscope, we find that particles show jump from sites to sites where they stay for a long time. This trap-jump process extremely decreases their mobility at low frequencies.