The present disclosure relates to a process for extracting sugars from a pretreated lignocellulosic biomass. This process consists of contacting the pretreated lignocellulosic biomass with low charges of an aqueous peroxy acid (PA) solution to produce a liquid fraction (containing a small amount of lignin and hemicellulose degradation products) and a solid fraction containing cellulose, hemicellulose and lignin. The solid fraction can then be subjected to enzymatic hydrolysis with a variety of cell wall-degrading enzymes to produce a lignin-rich residue and a sugar solution that can be fermented to a variety of (bio)chemicals.