Kraft lignin is an underutilized resource from the pulp and paper industry with the potential of being a key raw material for renewable fuels and chemicals. The separation of high-molecular-weight lignin from black liquor by ultrafiltration has been widely investigated, while the permeate containing low-molecular-weight lignin has received little attention. Nanofiltration can concentrate the low-molecular-weight lignin. This work, therefore, evaluates nanofiltration for the separation and concentration of low-molecular-weight lignin from the ultrafiltration permeate. For this study, eight flat polymeric sheet membranes and one polymeric hollow fiber membrane, with molecular weight cut-offs ranging from 100 to 2000 Da, were tested. A parametric study was conducted at 50 °C, 2.5–35 bar, and crossflow velocity of 0.3–0.5 m/s. At a transmembrane pressure of 35 bar, the best performing membranes were NF090801, with 90% lignin retention and 37 L/m²·h, and SelRO MPF-36, with 84% lignin retention and 72 L/m²·h. The other membranes showed either very high lignin retention with a very low flux or a high flux with retention lower than 80%. Concentration studies were performed with the two selected membranes at conditions (A) 50 °C and 35 bar and (B) 70 °C and 15 bar. The NF090801 membrane had the highest flux and lignin retention during the concentration studies. Overall, it was shown that the nanofiltration process is able to produce a concentrated lignin fraction, which can be either used to produce valuable chemicals or used to make lignin oil.