The segmental motions of flexible chains in the lamellar structure of a strongly segregated poly(styrene)-poly(dimethylsiloxane) (PS-PDMS) diblock were investigated over a time scale of a few tens of microseconds. (2)H NMR experiments were performed on the PDMS block, selectively perdeuterated. Transverse relaxation measurements show that the main part of the PDMS repeat units display anisotropic reorientational motions within the diblock lamellae and such a segmental ordering essentially results from interchain steric repulsions. (2)H double quantum-based experiments evidenced a non-uniform local stretching of PDMS chains and enabled the underlying distribution of the orientational order parameter to be determined quantitatively. Besides, a fraction of the PDMS chain segments, about 14%, were found to display isotropic - or nearly isotropic - reorientations, which could be assigned to repeat units located within a thin sublayer (about 1-2 nm) at the lamellae midplane, but also deeper in the lamellae, close to folded parts of the chains. These experimental results were confronted to theoretical descriptions of opposing polymer brushes and, in particular, to the strong-stretching theory (SST) including the entropic contribution of free chain ends.