Mechanical spectroscopy is used to probe the structure of lyotropic liquid crystalline polymers during flow and after the cessation of flow. The oscillatory flow is either parallel or perpendicular to the steady-state flow. The resulting moduli provide information about the time- and shear-dependent microstructure, including anisotropy. Two different concentrations of poly(benzylglutamate) (PBG) in m-cresol and a concentrated hydroxypropylcellulose (HPC) solution, also in m-cresol, are investigated. In all cases. the orthogonal superposition moduli evolve differently from the parallel ones. The former are less sensitive to the flow-induced changes in structure than the latter ones. Together with the lack of sensitivity of the superposition moduli to texture refinement during flow, this suggests a strong relation between director orientation and superposition moduli. After the cessation of flow the parallel moduli decrease for the PBG solutions, whereas the opposite is observed in the HPC solutions. A comparison with the orthogonal moduli provides a direct measure of anisotropy. At rest, the PBG solutions tend toward a higher degree of anisotropy while the HPC solutions become more isotropic. In the latter systems, all moduli are much larger, reflecting a larger contribution from the texture.