Lignin contributes to the rigid structure of the plant cell wall and is partially responsible for the recalcitrance of lignocellulosic materials to enzymatic digestion. Overcoming this recalcitrance is one the most critical issues in a sugar-flat form process. This study addresses the effect of low lignin sugarcane bagasse on enzymatic hydrolysis after liquid hot water pretreatment at 190 °C and 20 min (severity factor: 3.95). The hydrolysis of bagasse from a sugarcane line selected for a relatively low lignin content, gave an 89.7% yield of cellulose conversion to glucose at 40 FPU/g glucan versus a 68.3% yield from a comparably treated bagasse from the high lignin bred line. A lower enzyme loading of 5 FPU/g glucan (equivalent to 3.2 FPU/g total solids) resulted in 31.4% and 21.9% conversion yields, respectively, for low and high lignin samples, suggesting the significance of lignin content in the saccharification process. Further increases in the enzymatic conversion of cellulose to glucose were achieved when the bagasse sample was pre-incubated with a lignin blocking agent, e.g., bovine serum albumin (50 mg BSA/g glucan) at 50 °C for 1 h prior to an actual saccharification. In this work, we have demonstrated that even relatively small differences in lignin content can result in considerably increased sugar production, which supports the dissimilarity of bagasse lignin content and its effects on cellulose digestibility. The increased glucose yields with the addition of BSA helped to decrease the inhibition of non-productive absorption of cellulose enzymes onto lignin and solid residual lignin fractions.