The effects of a large strain (600%) reciprocating steady shear on the lamellar orientation and the order-disorder transition of a nearly symmetric poly(ethylene propylene)-poly(ethylethylene)-poly(ethylene propylene) (PEP-PEE-PEP) triblock copolymer have been studied using small-angle neutron scattering and rheological measurements. Shearing in the ordered state produced parallel lamellae under all steady-state conditions investigated, and the lamellar-to-disorder transition temperature decreased dramatically with increasing shear rate. Both phenomena are qualitatively different from the documented behavior of PEP-PEE diblock copolymers. However, cooling the disordered material while shearing at a relatively low deformation rate initially induces perpendicular lamellae, analogous to the diblock response. These observations are considered in the context of theory and other experimental studies.