The influence of the short alkyl-chain ionic surfactant OTAB on the dynamic behavior of an inverse block copolymer-rich lamellar phase was investigated by neutron spin-echo spectroscopy (NSE). The observed intermediate scattering function can be described by a sum of two contributions. For high scattering vectors the model of Zilman-Granek plus a slow diffusional mode can be used to describe the experimental data and the bending elastic modulus κ for a polymer-rich membrane is calculated. At low scattering vectors the relaxation curves are strongly influenced by de Gennes narrowing arising from the structure factor of the Lα phase. Hence, the computed relaxation rates in this q-range are inversely proportional to the static structure factor. The present study demonstrates the necessity to directly investigate the dynamic behavior of lamellar phases and that an analysis of the width of the Bragg peaks can be insufficient to derive information about the single membrane elasticity, especially when both κ and B[combining macron] depend on the composition of the membrane.