It has been widely documented that nematic and cholesteric liquid-crystalline materials can develop a one-dimensionally periodic microstructure subsequent to uniaxial draw, unidirectional shear, or injection moulding, This microstructure gives rise to a banded texture between crossed polars. A review of the literature, which contains many conflicting studies, identified several molecular and processing variables that may affect the rate of banded texture evolution. Our research focused on banded textures in three lyotropic systems of hydroxypropyl cellulose (HPC), a semiflexible polymer : HPC-water, HPC-methanol and HPC-acetone. Solutions were sheared unidirectionally with a motorized parallel-plate apparatus. The rate of band evolution after shear was quantified consistently in terms of the time taken for the average band spacing to reach a minimum, and was found to depend on a combination of prior shear rate, specimen thickness, solvent type and concentration. The dependence on solvent type is especially sensitive. The qualitative way in which these variables control the rate of microstructural change after shear is discussed in terms of (1) their effect on the ability of a sheared microstructure to store the energy that drives subsequent reordering and (2) their effect on the mobility of the microstructure.