In this study, novel Ga2O3/lignin and ZrO2/lignin hybrid materials were obtained and used as supports for the adsorption of the enzyme glucose oxidase (GOx). A biosensor system based on the hybrid supports was then designed to determine the concentration of glucose in various solutions. The obtained bioinspired platforms were analyzed to determine chemical and physical properties of the support structures. A determination was made of the effectiveness of the proposed method of immobilization and the quality of operation of the constructed glucose biosensor in electrochemical tests. To characterize the materials, Fourier transform infrared spectroscopy (FT-IR), transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray diffraction (XRD), thermogravimetric analysis (TGA), electrokinetic (zeta) potential measurements, atomic force microscopy (AFM), particle size measurements (NIBS technique), and elemental analysis (EA) were used. In further research, glucose oxidase (GOx) was immobilized on the surface of the obtained functional Ga2O3/lignin and ZrO2/lignin biomaterials. The best immobilization capacities—24.7 and 27.1 mg g−1 for Ga2O3/lignin and ZrO2/lignin, respectively—were achieved after a 24 h immobilization process. The Ga2O3/Lig/GOx and ZrO2/Lig/GOx systems were used for the construction of electrochemical biosensor systems, in a dedicated carbon paste electrode (CPE) with the addition of graphite and ferrocene.