We present the results of extensive strain- and stress-controlled rheometry performed on an AOT-water-iso-octane system, which forms lamellar structures with a high density of topological defects. In spite of different time-scales, both measurement methods, strain- and stress-controlled, are shown to be controlled by the level of strain experienced by the material. In both cases, after a complex transition, an apparent steady state is reached. Whereas both apparent steady states are identical for intermediate shear rate and shear stress following a power law, these are found to differ once the lower values of applied shear rate and shear stress are considered. The origin of this difference is discussed in terms of supplied energy to the sheared sample.