For the purposing of each lignin fraction in the lignin liquors, the development of separation strategies to fractionate the lignin streams by MW ranges constitutes a timely challenge to be tackled. Herein, membrane separation was applied to the refining of lignin streams obtained from a lignin-first biorefining process based on H-transfer reactions catalyzed by Raney Ni, using 2-propanol 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 CUB liquor. Building on the experimental results, an economic evaluation of the potential of membrane separation for the refining of lignin streams was undertaken. The membrane performance represents the bottleneck of the costs associated with the separation process. Accordingly, we present a detailed analysis of future developments in the performance required to debottleneck the utilization of membrane separation for lignin refining.