We report a comprehensive study on mechanotransmission of shear forces across lipid bilayer membranes of giant unilamellar vesicles (GUVs). GUVs containing fluorescent tracer particles were immobilized on a microfluidic platform and exposed to shear flows. A method was developed for the visualization of three-dimensional flows at high precision by defocusing microscopy. We quantify the symmetry of external flow around the GUV and show its effects on vortex flows and luminal dynamics. With increasing asymmetry, luminal vortices merged while liquid exchange in between them increased. The effect of membrane composition was studied through addition of cholesterol. Mechanotransmission efficacy, quantified by the ratio of luminal flow to external flow, ranged from ε = 0.094 (0 mol % cholesterol) to ε = 0.043 (16 mol % cholesterol). Our findings give new cues to the mechanisms underlying the sensing of strength and spatial distribution of shear forces by cells and the impact of membrane composition.