The shear rate min, at the relative minimum in the N-1 flow curve is studied as a function of temperature and concentration for liquid crystalline (hydroxypropyl)cellulose (HPC). For lyotropes, at least, gamma(min) is the shear rate necessary to halt director "tumbling" and align the molecules. HPC is a convenient polymer for studying the relationship between lyotropic and thermotropic liquid crystalline polymers because it exhibits a pure thermotropic phase at elevated temperatures, and room temperature lyotropic phases at moderate concentrations in m-cresol. At the highest possible polymer concentration at which reliable rheology data can be obtained (around 70 wt % polymer), indirect evidence for director tumbling is observed, in that N-1 retains a local minimum versus shear rate. For the highest concentrations this minimum N1 value is positive, rather than negative, as is the case at lower concentrations and as is predicted by the Doi theory. Empirical time-temperature and time-concentration shifting can be used to estimate gamma min from measured values of the shear viscosity.