The sustainability, performance, and cost of production in the plywood industry depend on wood adhesives and the hot-pressing process. In this study, a cold-setting plywood adhesive was developed based on polyvinyl alcohol (PVOH), high-purity lignin, and hexamine. The influence of lignin content (10%, 15%, and 20%) and cold-pressing time (3, 6, 12, and 24 h) on cohesion, adhesion, and formaldehyde emission of plywood were investigated through physical, chemical, thermal, and mechanical analyses. The increased lignin addition level lowered the solids content, which resulted in reduced average viscosity of the adhesive. As a result, the cohesion strength of the adhesive formulation with 10% lignin addition was greater than those of 15% and 20% lignin content. Markedly, the adhesive formulation containing a 15% lignin addition level exhibited superior thermo-mechanical properties than the blends with 10% and 20% lignin content. This study showed that 10% and 15% lignin content in the adhesive resulted in better cohesion strength than that with 20% lignin content. However, statistical analysis revealed that the addition of 20% lignin in the adhesive and using a cold-pressing time of 24 h could produce plywood that was comparable to the control polyurethane resins, i.e., dry tensile shear strength (TSS) value of 0.95 MPa, modulus of rupture (MOR) ranging from 35.8 MPa, modulus of elasticity (MOE) values varying from 3980 MPa, and close-to-zero formaldehyde emission (FE) of 0.1 mg/L, which meets the strictest emission standards. This study demonstrated the feasibility of fabricating eco-friendly plywood bonded with PVOH–lignin–hexamine-based adhesive using cold pressing as an alternative to conventional plywood.