This study reports the synthesis of polyurethane–lignin copolymer blended with carbon multilayer nanotubes to be used in all-solid-state potentiometric chemical sensors. Known applicability of lignin-based polyurethanes doped with carbon nanotubes for chemical sensing was extended to eucalyptus LignoBoost® kraft lignin containing increased amounts of polyphenolic groups from concomitant tannins that were expected to impart specificity and sensitivity to the sensing material. Synthesized polymers were characterized using FT-MIR spectroscopy, electrical impedance spectroscopy, scanning electron microscopy, thermogravimetric analysis, and differential scanning calorimetry and are used for manufacturing of all solid-state potentiometric sensors. Potentiometric sensor with LignoBoost® kraft lignin-based polyurethane membrane displayed theoretical response and high selectivity to Cu (II) ions, as well as long-term stability.