The formation of multilamellar vesicles (MLVs) from the lamellar phase of nonionic surfactant system C12E5/D2O under shear flow is studied by time-resolved small angle neutron and light scattering during shear flow. A novel small angle neutron scattering sample environment enables the tracking of the lamellae alignment in the velocity-velocity gradient (1-2) plane during MLV formation, which was tracked independently using flow small angle light scattering commensurate with rheology. During the lamellar-to-multilamellar vesicle transition, the primary Bragg peak from the lamellar ordering was observed to tilt, and this gradually increased with time, leading to an anisotropic pattern with a primary axis oriented at similar to 25 degrees relative to the flow direction. This distorted pattern persists under flow after MLV formation. A critical strain and critical capillary number based on the MLV viscosity are demonstrated for MLV formation, which is shown to be robust for other systems as well. These novel measurements provide fundamentally new information about the flow orientation of lamellae in the plane of flow that cannot be anticipated from the large body of previous literature showing nearly isotropic orientation in the 2,3 and 1,3 planes of flow. These observations are consistent with models for buckling-induced MLV formation but suggest that the instability is three-dimensional, thereby identifying the mechanism of MLV formation in simple shear flow.