We report a study of the shear response of sponge phases in cetylpyridinium chloride (CPCI)/hexanol/ brine/dextrose systems by parallel measurements of rheology and structure by small angle neutron scattering (SANS). Our measurements show that this dextrose added to the extensively studied CPCl/hexanol/brine system is taken up exclusively by the brine solvent, resulting in an equivalent CPCl/hexanol membrane structure and phase behavior for this modified system. Adding dextrose to the brine in these systems to volume fractions up to 0.4 allows us to increase the solvent viscosity by more than an order of magnitude. This lowers the cooperative membrane diffusion coefficient in this system as measured by dynamic light scattering by the same factor, resulting in a corresponding slowing of the Helfrich fluctuation dominated membrane dynamics. Our results show clear and consistent evidence of shear-induced sponge to lamellar phase transformations in these systems. Further, both the rheological and microstructural responses of these systems follow universal master curves when plotted against a rescaled applied shear gammaeta(s)/phi(3), where phi is the membrane volume fraction and eta(s) is the viscosity of the brine/dextrose solvent. This well-defined shear response is characterized by three distinct regimes. At low shear rates the sponge phases exhibit Newtonian flow behavior and no structural change is observed. For intermediate shear rates, the systems shear thin and SANS measurements show that the sponge phases are progressively transformed into lamellar phases with the CPCl/hexanol membrane normals aligned parallel to the velocity gradient. This continuous process and the absence of a stress plateau in the rheological measurements both rule out the existence of a biphasic state in this region and thus of a first-order transition between sponge and lamellar phases as is observed in equilibrium phase diagrams. At higher shear rates, the systems are apparently again Newtonian, but the induced lamellar phase appears to collapse and a new (and as yet unidentified) large-scale structure forms. We have found these systems to be extremely sensitive to evaporation, and reproducibility of the scattering measurements required the use of a Couette shear cell with a specially designed vapor barrier.