In this study, a biobased phenolic adhesive was successfully developed by entirely substituting both petroleum-based phenol and formaldehyde with an unmodified corn stover biorefinery lignin and glyoxal (a biobased dialdehyde), respectively. Lignin-glyoxal resins were synthesized using an alkaline catalyst with a molar ratio of lignin to glyoxal of 1:2. Chemical, thermal, and mechanical properties of the lignin, lignin-based resins, and final adhesives were assessed following appropriate standard test methods. The analysis of lignins and lignin-based resin molar mass was performed using gel permeation chromatography. The lignin-glyoxal resin was found to have a 3-fold higher average molecular weight than the starting lignin, demonstrating the successful integration of lignin into the polymeric resin network. The curing of the formulated adhesives was studied using differential scanning calorimetry and dynamic mechanical analysis. Although the lignin-glyoxal resin had a higher curing temperature (167 °C) than a conventional phenol-formaldehyde resin (142 °C) and the formulated lignin-formaldehyde resin (146 °C), the rate and degree of cure were similar or better than the other two resins. The adhesion strengths of the formulated adhesives were determined using single-lap-joint veneer samples cured according to recommended press parameters for commercial adhesives. The lignin-glyoxal adhesive had a relatively high dry adhesion strength (3.9 MPa), with over 90% wood failure, but failed the wet adhesion test (boiling water test). Although the formulated lignin-glyoxal adhesive failed the boiling water test, it had excellent stability at room temperature water, remaining intact after 1 week during the water immersion test. The high dry adhesion strength makes this class of lignin-based formaldehyde-free adhesives a unique biobased glue for the production of interior grade plywood and oriented strand boards.