<p>To investigate the dynamic properties of fiber-reinforced sand, this study used natural sand from the Tarim Basin in Xinjiang as the research object. Meanwhile, in response to the dual-carbon strategy, environmentally friendly and biodegradable natural biomass lignin fibers were selected as the modification material. Dynamic strength tests with different fiber contents were conducted via cyclic triaxial tests, and the liquefaction resistance and dynamic strength indices of the reinforced sand under different confining pressures, consolidation ratios, and vibration frequencies were comparatively analyzed. The results show that the fiber content and consolidation ratio significantly affect the dynamic strength of sand: with the increase in vibration frequency, the viscoelastic hysteresis effect of the fiber material weakens the improvement effect at high frequencies. Based on the test data, a multi-variable nonlinear model for the dynamic internal friction angle—considering fiber content (<i>F</i>_c), consolidation ratio (<i>K</i>_c), vibration frequency (<i>f</i>), and number of vibrations (<i>N</i>)—was established. The model has an <i>R</i>² of 0.980 and an RMSE of 0.794°. Verification results indicate that the model’s prediction accuracy meets engineering requirements within the range of conventional parameters. The research findings can provide a theoretical basis for the seismic design of lignin fiber-reinforced sand foundations.</p>