In this study, we report on the visco-elastic response during start-up and cessation of shear of a novel bio-based liquid crystal polymer. The ensuing morphological changes are analyzed at different length scales by in-situ polarized optical microscopy and wide-angle X-ray diffraction. Upon inception of shear, the polydomain texture is initially stretched, at larger strain break up processes become increasingly important, and eventually a steady state texture is obtained. The shear stress response showed good coherence between optical and rheo-X-ray data. The evolution of the orientation parameter coincides with the evolution of the texture: the order parameter increases as the texture stretches, drops slightly in the break up regime, and reaches a constant value in the plateau regime. The relaxation of the shear stress and the polydomain texture showed two distinct processes with different timescales: The first is fast contraction of the stretched domain texture; the second is the slow coalescence of the polydomain texture. The timescale of the orientation parameter's relaxation matched with that of the slow coalescence process. All processes were found to scale with shear rate in the tested regime. These observations can have far reaching implications for the processing of liquid crystal polymers as they indicate that increased shear rates during processing can correspond to an increased relaxation rate of the orientation parameter and, therefore, a decrease in anisotropy and material properties after cooling.