We present a first investigation about the non-linear flow properties and transient orientational-order fluctuations observed in the shear-thinning lecithin-water-cyclohexane wormlike micellar system at a concentration near to the zero-shear isotropic-nematic phase transition. From rheological measurements the stress plateau was found shifted to very low values of the applied shear rate gamma, compared to most of the concentrated living polymer systems reported in the literature. Rheo-small angle neutron scattering (Rheo-SANS) experiments performed in the flow-vorticity plane revealed periodical fluctuations of both the order parameter P(2) and the angular deviation phi from the vorticity axis as determined from the scattering peaks. The periods of the oscillations were not found to depend on imposed gamma. A theoretical model was also developed to explain the oscillatory dynamics of the shear-induced nematic order parameter in terms of the presence of standing waves of the director orientation profile along the circumference of the Couette cell. The experimental results of the periodic order parameter fluctuations together with their theoretical modelling shed significant new insights on the shear banding phenomenon, particularly its microscopic mechanism.