A microstructural lattice simulation for textured liquid crystalline polymer is carried out to predict rheological behavior, especially the stress evolution after shear inception. It is based on a combination of two main concepts: (i) the director in each cell of a supramolecular lattice has an orientation described by the minimization of total energy of director map, and (ii) the torque balance of each director under shear flow and anisotropic relaxational shear moduli depends on the averaged orientation of the director map. By considering the interaction between the nearest-neighbor directors, the spatial orientational correlation is introduced and the spatial heterogeneity, i.e., a polydomain texture, is generated simultaneously. For the start-up shear flow, the overshoot and the steady value of shear stress increase and the former shifts toward a shorter time as the applied shear rate increases. Also, the calculated stress evolution is compared with the experimental result of a thermotropic liquid crystalline poly(ester-imide).