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Lipid membranes in nature adapt and reconfigure to changes in composition, temperature, humidity, and mechanics. For instance, the oscillating mechanical forces on lung cells and alveoli influence membrane synthesis and structure during breathing. However, despite advances in the understanding of lipid membrane phase behavior and mechanics of tissue, there is a critical knowledge gap regarding the response of lipid membranes to micromechanical forces. Most studies of lipid membrane mechanics use supported lipid bilayer systems missing the structural complexity of pulmonary lipids in alveolar membranes comprising multi-bilayer interconnected stacks. Here, we elucidate the collective response of the major component of pulmonary lipids to strain in the form of multi-bilayer stacks supported on flexible elastomer substrates. We utilize X-ray diffraction, scanning probe microscopy, confocal microscopy, and molecular dynamics simulation to show that lipid multilayered films both in gel and fluid states evolve structurally and mechanically in response to compression at multiple length scales. Specifically, compression leads to increased disorder of lipid alkyl chains comparable to the effect of cholesterol on gel phases as a direct result of the formation of nanoscale undulations in the lipid multilayers, also inducing buckling delamination and enhancing multi-bilayer alignment. We propose this cooperative short- and long-range reconfiguration of lipid multilayered films under compression constitutes a mechanism to accommodate stress and substrate topography. Our work raises fundamental insights regarding the adaptability of complex lipid membranes to mechanical stimuli. This is critical to several technologies requiring mechanically reconfigurable surfaces such as the development of electronic devices interfacing biological materials.