Lignin is an abundant biopolymer, as well as cellulose and hemicellulose. Thus, this work aimed at isolating and characterizing the lignin from Eucalyptus spp. Sawdust—a lignocellulosic waste generated in large amounts in sawmills—to evaluate its antioxidant capacity. A biorefinery perspective was utilized: the biomass was fractionated using a sequential acid-alkaline treatment to recover the hemicellulosic carbohydrates, preserving the cellulose-rich solid fraction and isolating the lignin. The physicochemical characterization of isolated lignin was carried out using thermogravimetric (TGA), Fourier-transform infrared spectroscopy (FTIR), and nuclear magnetic resonance (NMR) analyses, while the antioxidant property was evaluated employing electron transfer and using DPPH and ABTS assays. After sequential acid-alkaline treatment, 68.15% of the hemicellulosic carbohydrates were recovered using mild acid treatment. The specific yield of lignin was 69.38%, and the remaining solid fraction contained 60.42% of cellulose. The antioxidant activity of lignin was evaluated using a DPPH radical test, and it showed an inhibition of 81.58% and IC50 of 60 μg/mL. For the ABTS test, the inhibition was 99.86%, and the IC50 was 7.39 µg/mL. Therefore, the lignin isolated from residual eucalyptus sawdust using sequential acid-alkaline treatment presented interesting antioxidant properties, which should be further investigated and evaluated for different applications.