The influence of a triblock copolymer, poly(ethylene oxide)(20)-b-poly(propylene oxide)(70)-b-poly(ethylene oxide)(20) (Pluronic P123) on the phase behavior and on the shear-induced multilamellar vesicle (MLV, also called Onion) formation in the lyotropic lamellar phase of the nonionic surfactant C10E3 was investigated by means of rheology, small-angle neutron scattering (SANS), and microscopy. Added triblock copolymer shifted the L-alpha-L-3 phase transition to lower temperatures. In the presence of triblock copolymer, MLV structure was not stable and easily transformed back into the lamellar phase with increasing polymer concentration and temperature. In the study of the shear-induced MLV formation, we found an increase of the critical shear rate for the onset of the shear-thickening, which also indicates the instability of MLV in the presence of the triblock copolymer. No MLV formation was observed at high polymer concentration. Suppression of the shear-induced MLV formation might be attributed to the enhancement of the effective surface tension originating from the excluded volume effect between polymers adsorbed onto the membranes.