To utilize lignin, which is a sustainable natural polymer, a star-like lignin-graft-polyethylene glycol methacrylate–glycidyl methacrylate (LGPG) polymer was prepared via solvent extraction and atom transfer radical polymerization (ATRP). Ethyl acetate-extracted lignin, obtained from the solvent extraction of Kraft lignin (KL), exhibited higher reactivity in ATRP, resulting in the synthesis of a star-like structure with a higher degree of polymerization than KL. The resulting LGPG/poly(ethylene oxide) (PEO) composite membranes exhibited high thermal stability and excellent elongation at break of 598.56% (with 0.3 g of LGPG). These findings indicated that LGPG imparted more flexible properties to the membranes than those made solely of PEO. Moreover, the addition of LGPG to the composite membrane decreased the glass transition temperature and crystallinity. These results indicated a plasticizing effect due to the high free volume and flexible multiarm structure of the star-like polymer, which disrupted the PEO chain packing within the membrane. This plasticizing effect resulted in LGPG/PEO composite membranes with high ionic conductivity when used as solid polymer electrolytes (SPEs). Furthermore, the performance of coin cells using LGPG/PEO composite membranes in lithium–lithium symmetric cell lithium plating/stripping tests revealed a lower and more stable voltage profile than that of the PEO membrane following 50 charge/discharge cycles. This study highlights the potential of ATRP as a favorable method for synthesizing SPEs using lignin in electrochemical applications.