We use standing surface acoustic waves to induce coherent phonons in model lipid multilayers deposited on a piezoelectric surface. Probing the structure by phase-controlled stroboscopic x-ray pulses we find that the internal lipid bilayer electron density profile oscillates in response to the externally driven motion of the lipid film. The structural response to the well-controlled motion is a strong indication that bilayer structure and membrane fluctuations are intrinsically coupled, even though these structural changes are averaged out in equilibrium and time integrating measurements. Here the effects are revealed by a timing scheme with temporal resolution on the picosecond scale in combination with the sub-nm spatial resolution, enabled by high brilliance synchrotron x-ray reflectivity.