Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in Hønger et al. [Phys. Rev. Lett. 72, 3911 (1994)].PACS. 87.16.-b Subcellular structure and processes -64.70.Md Transitions in liquid crystals -61.10.Eq X-ray scattering (including small-angle scattering)