Parallel superposition moduli have been measured on a lyotropic liquid crystal, i.e., poly(benzyl-L-glutamate) in m-cresol. The objective of the work is to elucidate the mechanisms that determine the elastic response as measured by the storage moduli in the material under consideration. Superposition moduli have been obtained in the Newtonian and in the shear thinning regions. The ones in the Newtonian region are independent of shear rate and are identical to those obtained immediately after cessation of flow. The results are compared with the time evolution of the moduli after stopping the flow. Also other rheological and rheo-optical evidence is used to evaluate the structural changes during flow. It is concluded that the dynamic moduli are not controlled by domain size and consequently Frank elasticities do not play a direct role. Molecular ordering and orientation, integrated over the domains, is retained to explain the oscillatory elastic response. This is in agreement with all available data. The Frank elasticities still might control the time evolution of the moduli after stopping the flow. The present results prove that the Larson-Mead analysis has a physically sound structural basis.