Lignocellulose is one of the most promising renewable bioresources for the production of chemicals. For sustainable and competitive biorefineries, effective valorization of all biomass fractions is crucial. However, current efforts in lignocellulose fractionation are limited by the use of either toxic or suboptimal solvents that do not always allow producing clean and homogeneous streams. Here, we present a computational screening approach that covers more than 8000 solvent candidates for the processing of lignocellulosic biomass. The automated screening identified highly effective, non-intuitive solvents based on physico-chemical properties, solubilities of the biomass fractions, and environmental, health and safety properties. Solubility experiments for the lignin and cellulose fraction confirmed the applicability of the proposed framework in biomass processing. In addition to the traditional "lignin-first'' approaches, we identified solvents applicable for the complete dissolution of biomass. Furthermore, we elucidated particular structural patterns in solvents featuring high lignin solubility. The most promising solvents attained lignin solubilities of more than 33 wt%.