By means of computer simulations, we investigate the segmental dynamics in the lamellar phase of a simple bead-spring model of diblock copolymers. We characterize the dynamic heterogeneity in the mean-squared displacements and bond reorientations. This characterization is made as a function of both the position of the monomers along the chain and the distance to the nearest interface between consecutive domains. Both characterizations of the dynamic heterogeneity reveal moderate gradients of mobility in the investigated temperature range, which qualitatively probes relaxation time scales of up to hundreds of nanoseconds. Namely, the obtained distribution of relaxation times spreads over about 1 decade. However, the extrapolation of the former analysis to lower temperatures leads to an increasing spread over several time decades. The spread mostly arises from monomers located at the immediate neighborhood of the interface. Beyond such distances the structural relaxation approaches that of the homopolymer. Thus, the observed dynamic heterogeneity is esentially an interfacial effect. It does not originate from gradients of density over the domains. Indeed such gradients are absent, and the local density within the domains is identical to that of the corresponding homopolymers.