A low-cost process is provided to render lignocellulosic biomass accessible to cellulase enzymes, to produce fermentable sugars. Some variations provide a process to produce ethanol from lignocellulosic biomass (such as sugarcane bagasse or corn stover), comprising introducing a lignocellulosic biomass feedstock to a single-stage digestor; exposing the feedstock to a reaction solution comprising steam or liquid hot water within the digestor, to solubilize the hemicellulose in a liquid phase and to provide a cellulose-rich solid phase; refining the cellulose-rich solid phase, together with the liquid phase, in a mechanical refiner, thereby providing a mixture of refined cellulose-rich solids and the liquid phase; enzymatically hydrolyzing the mixture in a hydrolysis reactor with cellulase enzymes, to generate fermentable sugars; and fermenting the fermentable sugars to produce ethanol. Many alternative process configurations are described. The disclosed processes may be employed for other fermentation products.