Biological membranes approach one another in various biological phenomena, such as lipid transport at membrane contact sites and membrane fusion. The proximity of two bilayers may cause environmental changes in the interbilayer space and alter the dynamics of lipid molecules. Here, we investigate the structure and dynamics of vesicles aggregated due to the depletion attraction caused by polyethylene glycol (PEG) through static and dynamic small-angle neutron scattering. Manipulation of the interbilayer distance using PEG-conjugated lipids reveals that lipid molecules rapidly transfer between vesicles when the opposing bilayers are within ∼2 nm of each other. This distance corresponds to a region in which water molecules are more structured than in bulk water. Kinetic analysis suggests that the decrease in water entropy is responsible for the progression of lipid transfer. These results provide a basis for understanding the dynamic function of biomembranes in confined regions.