In this study, unmodified kraft softwood lignin was utilized to fully replace the petroleum-based polyol for the first time in low-density rigid polyurethane/polyisocyanurate (PUR/PIR) foam. The effects of different lignin incorporation levels (0, 25, 50, 75, and 100%) on foam properties were investigated by measuring foam's reactivity, polyol viscosity (using a rheometer), apparent density, compression strength, closed cell content (using a gas pycnometer), thermal conductivity, fire resistance, and morphology (observed through SEM). All formulated lignin-based foams met the ASTM minimum requirements for type 1 rigid insulation foams. Remarkably, the foam made by replacing 100% of the petrochemical polyol with the commercially available kraft lignin demonstrated outstanding fire resistance performance, reducing the burn length by 127%.