The long-wave dynamics of an elastic sheet lubricated by a thin layer of viscous fluid on a wetting substrate is examined using both numerical simulations and a quasistatic model. As a continuum model for a lipid bilayer, the elastic sheet has a electric capacitance that stores changes across the membrane. Within the lubrication framework we investigate the electrohydrodynamics of the thin film coupled to the capacitive elastic membrane. Novel nonlinear dynamics is found and results are useful to understand electroformation, a standard experimental procedure to fabricate unilamellar vesicles from planar lipid bilayer membrane. We also extend this theoretical framework to investigate the rupture of vesicles when settled onto a glass substrate in an ionic solution.