For the utilization of each lignin fraction in the lignin liquors, the development of separation strategies to fractionate the lignin streams by molecular weight ranges constitutes a timely challenge to be tackled. Herein, membrane filtration was applied to the refining of lignin streams obtained from a lignin‐first biorefining process based on H‐transfer reactions catalyzed by Raney Ni, by using 2‐PrOH as a part of the lignin extraction liquor and as an H‐donor. A two‐stage membrane cascade was considered to separate and concentrate the monophenol‐rich fraction from the liquor. Building on the results, an economic evaluation of the potential of membrane filtration for the refining of lignin streams was undertaken. In this proof‐of‐concept report, a detailed analysis is presented of future developments in the performance required for the utilization of membrane filtration for lignin refining and, more aspiringly, solvent reclamation.