Digestion of cellulosic biomass solids may be complicated by lignin release therefrom, which can produce a highly viscous phenolics liquid phase comprising lignin polymer. Methods for digesting cellulosic biomass solids may comprise: providing cellulosic biomass solids in the presence of a digestion solvent, molecular hydrogen, and a slurry catalyst capable of activating molecular hydrogen; at least partially converting the cellulosic biomass solids into a phenolics liquid phase comprising lignin, an aqueous phase comprising an alcoholic component derived from the cellulosic biomass solids, and an optional light organics phase; wherein at least a portion of the slurry catalyst accumulates in the phenolics liquid phase as it forms; and reducing the viscosity of the phenolics liquid phase.