The self-diffusion properties of a poly(styrene-b-isoprene) diblock copolymer (M-PS = 10000, M-PI = 13000) in a lamellar microstructure have been determined by forced Rayleigh scattering. Diffusion coefficients along the lamellar interface (D-par) and through the layers (D-perp) were resolved. The lamellae were macroscopically oriented using large amplitude oscillatory shear; small-angle X-ray scattering and transmission electron microscopy confirmed a high degree of alignment. The measured anisotropy of mobility was surprisingly large at 90 degrees C : D-par/D-perp approximate to 40. However, at 110 degrees C the anisotropy decreased by an order of magnitude. This reduction is only partly attributable to the approaching order-disorder transition (at 160 degrees C); the strong temperature dependence of the styrene monomeric friction factor in styrene-rich domains is also implicated. Further measurements were made on a copolymer with half the total molecular weight (M-PS = 5000, M-PI = 6500), which was in the disordered state over the temperature range of interest. These data confirm the importance of the composition and temperature dependences of the monomeric friction factors, coupled with the spatial homogeneity/heterogeneity of the average composition. The results are discussed in terms of proposed mechanisms of diffusion in block copolymer microstructures.