The dynamics of diblock copolymers organized into a lamellar microstructure has been simulated on a cubic lattice. The chains of A10B10 are present at a volume fraction of 0.847 and the reduced pairwise interaction energy between A and B is 0.5, which places the system near the microphase separation transition. Parallel simulations were performed in which the voids participated in no interactions with either block and in which they behaved as monomeric species of B. The motion is monitored for the beads at the free ends of both blocks and for the beads at the junction between the blocks. At short times, the beads at the free ends experience greater motion than the beads at the junction points. The trajectory was long enough to estimate the self-diffusion coefficient for the chains in the system where the voids do not participate in interactions with either block. This self-diffusion coefficient could be decomposed into components in the plane of the lamellae and normal to the interface. These components differ by an order of magnitude, with the slower diffusion being in the direction normal to the plane of the interface. The bond autocorrelation function decays quickly to zero for the bonds at the free ends, but it does not decay to zero on the time scale of the simulations for the bond at the junction between the two blocks.