We use molecular dynamics simulations to study the normal mode dynamics and frequency dependent dielectric relaxation spectra of diblock copolymers in lamellar phases. In contrast to previous works which have relied on the applicability of Rouse modes, we effect an explicit normal-mode analysis of the chain dynamics in the ordered phases in the directions parallel and perpendicular to the lamellar plane. We considered two models to isolate the specific effects arising from the morphological ordering and mobility disparities between the blocks. For systems with no mobility disparity between the blocks, our analysis demonstrates that both the normal modes and their relaxation dynamics in the planes parallel and perpendicular to the lamella exhibit deviations from the Rouse modes. For systems in which the mobility of one of the blocks was frozen in the lamellar phase, the normal modes closely resembled the Rouse modes for tethered polymers. However, the relaxation dynamics of such modes exhibited deviations from expectations for tethered chains. The changes in the normal mode dynamics manifest as shifts and broadening of the normal dielectric spectra. Together, our results serve to clarify the dielectric spectra effects resulting from the ordering of diblock copolymers into self-assembled morphologies.