This study aimed to develop new rigid polyurethane foams (RPUFs) for thermal insulation based on kraft lignin, the main by-product of the pulp and paper industry. Crude lignin-based polyol (LBP) was obtained via the oxyalkylation of kraft lignin using propylene carbonate (PC). A design of experiments (DoE) was used to evaluate the effect of the isocyanate (NCO)-to-hydroxyl (OH)-group’s ratio, the content of crude LBP, the blowing agent (BA), and catalyst on the thermal conductivity and density of RPUFs. Statistical analysis revealed that the increase in crude LBP and BA content in the formulation decreases the thermal conductivity and density of the foams. In addition, the fact that LBP is a viscous polyol containing PC-oligomers appears to affect the cellular structure of RPUFs, and consequently reduces their mechanical and thermal properties. The main novelty of this study consisted in the careful optimization of the formulation, namely, with regard to the type of blowing agent and with the high content of crude LBP obtained from the oxyalkylation of LignoBoost kraft lignin without purification to obtain good quality RPUF that meets market requirements for insulation materials.