The nonequilibrium dynamics of a fluid lipid membrane under external stimuli is an important issue that spans disciplines such as soft matter, biophysical chemistry, and interface science. This study investigated the dynamic response of lipid vesicles with order-disorder phase separation, which mimics a plasma membrane heterogeneity, to shear flow. Lipid vesicles were immobilized in a microfluidic chamber, and shear-induced nonequilibrium patterns on the membrane surface were observed by an optical microscope. We found that phase-separated membranes exhibit a dissipative structure of stripe patterns along the vortex flow on the membrane surface, and the number of stripes increased with the flow rate. At a high flow rate, the membrane exhibited a stripe-to-wave transition, where striped domains often migrated and the replacement of two different phases happened at vortex centers with time. We obtained a dynamic phase diagram of the shear-induced wave pattern by changing the flow rate, membrane components, and temperature. These findings could provide insight into the dissipative structures of lipid membranes out of equilibrium and flow-mediated mechanotransduction of biological membranes.