To enhance the high-value utilization of straw waste and achieve efficient lignin extraction, wheat straw was selected as the feedstock for investigating the effects of reaction temperature, reaction time, solid–liquid ratio, and formic acid concentration on lignin yield using a formic acid/acetic acid solvent system. A single-factor experimental design was initially employed, followed by optimization using the response surface methodology. Additionally, a kinetic model was developed to describe lignin extraction kinetics in the formic acid/acetic acid system. The structural characteristics and thermal stability of the extracted lignin were analyzed via FTIR, UV spectroscopy, and TGA. The findings indicate that increasing reaction temperature, reaction time, solid–liquid ratio, and formic acid content all significantly enhanced lignin extraction yield from wheat straw, with the primary influencing factors being reaction temperature > solid–liquid ratio > reaction time > formic acid content. The optimal extraction conditions were identified at a reaction temperature of 90 °C, a reaction time of 3.5 h, a solid–liquid ratio of 1:16.5, and a formic acid content of 86.2 wt.%, yielding a lignin content of 79.83%. The analytical results demonstrated that the extracted lignin preserved the structural integrity of the original lignin and exhibited good thermal stability.