Shear flow is a versatile strategy to align microphase-separated morphologies of diblock copolymers over macroscopic scales. Details of the local mechanism of reorientation toward the steady, nonequilibrium state, however, are only incompletely understood. Using large scale molecular simulation as well as experiments, we study the shear-alignment mechanism using lamella-forming, symmetric, unentangled diblock copolymers in steady and oscillatory shear flow. First we study homogeneously oriented systems and investigate the stability of different orientations with respect to the shear flow by the Rayleighian. Second, we investigate the process of reorienting an unstable grain with parallel orientation embedded in a matrix of stable, perpendicularly oriented lamellae. We observe two different reorientation mechanisms as a function of the shear rate: a fast transition, which is comparable to experimental conditions in large-amplitude oscillatory shear (LAOS) tests, and a slower transition occurring at lower shear rates. We show that for high shear rates the long-range orientational order of the lamellae inside the unstable grain disintegrates, while the grain remains spatially structured with the same characteristic length scale (similar to a microemulsion). At lower shear rates, however, we observe a shrinking of the unstable grain, i.e., a directed movement of the grain boundaries. Additionally, we compare the results of steady shear with oscillatory shear.