We evaluate the effects of an applied electric potential on the adsorption/desorption mechanism of cationic nanoparticles on lipid membranes. By applying a molecular theory that allows calculating nanoparticle adsorption isotherms and free-energy profiles, we identify the conditions under which the external voltage promotes the adsorption of nanoparticles coated with cell penetrating peptides. We consider symmetric and asymmetric membranes made of neutral and acidic lipids and cover a wide range of environmental conditions (external voltage, pH, salt, and nanoparticles concentration) relevant to both electrochemical experiments and biological systems. For neutral membranes at low concentration of salt, a moderate external voltage (<100 mV) induces spontaneous adsorption of nanoparticles. For membranes containing a small fraction of anionic lipids, the external potential has little effect on the interfacial concentration of nanoparticles, and the membrane surface charge dominates the adsorption behavior. In all cases, the membrane-particle effective interactions, and its dependence on the external bias, are strongly modulated by the concentration of salt. At 100 mM NaCl, the external potential has almost no effect on the adsorption free energy profiles. In general, we provide a theoretical framework to evaluate the conditions under which nanoparticles are thermodynamically adsorbed or kinetically restrained to the vicinity of the membrane, and to assess the impact of the nanoparticles on the interfacial electrostatic properties.