In water, the nonionic surfactant pentaethylene glycol monododecyl ether (C12E5) forms multi-lamellar vesicles upon application of shear, attributed to buckling instability of the surfactant layers. In the standard setup for applying shear, a pair of solid substrates is moved in opposite directions, and a non-slip condition at the solid surface is assumed. Based on theoretical predictions, the effective viscosity of the fluid surrounding the membrane is modified in this process, and this confinement may affect membrane fluctuation. However, only a few studies have analyzed the structural changes near the substrate. From this viewpoint, the structural changes in surfactant aggregates near a solid substrate under the application of shear were investigated herein using neutron reflectometry (NR). By increasing the shear rate, shear thickening at a lower shear rate and shear thinning at a higher shear rate were observed, similar to that in the bulk. However, a discontinuous change in the lamellar structure accompanying the condensation of the surfactant was observed in the NR experiments. This study presents the first experimental evidence indicating that the ramping speed of shear rates governs the shear-induced structuring of surfactant aggregates near the surface.