Robust and electrochemically stable electrodes are critical for emerging energy storage devices. In this work, we describe the synthesis and characterization of an asymmetric pseudocapacitor with a P(nBA-stat-BzMA)/reduced graphene oxide (rGO, 5 wt %) nanocomposite cathode incorporating a low content of lignosulfonate (LS, 5 wt %) and a P(nBA-stat-BzMA)/rGO anode. Besides the advantageous green source and low cost of LS, its properties as a binder and its redox groups contribute to the electrochemical performance improvement of the pseudocapacitor. First, the electrochemical optimization and characterization of an asymmetric unit cell is performed. Subsequently, a series of 10 unit cells are arranged in a “stack of cells”; electrochemical tests show this assembly to have a capacitance of 4.90 F cm–3 (8.60 F g–1), maximum power of 610 W kg–1, energy of 4.32 W h kg–1, loss of electroactivity of 1.8%, capacitance retention of 98%, and Coulombic efficiency of 108% after 1000 charge–discharge cycles at a constant current of 0.12 A cm–3. Morphological analysis revealed an increase in surface roughness after LS incorporation within the cathode. Electrode–electrolyte resistances were calculated via electrochemical impedance spectroscopy, which allowed us to propose a model of electrode–electrolyte interaction for this system.