Skeletal muscles exhibit excellent properties due to their well-developed microstructures. Taking inspiration from nature that thick filaments and thin filaments are linked by “cross-bridges”, leading to good stability and ion transport performance of muscles. In this work, extracted poplar lignin and microcrystalline cellulose (MCC) were connected by biomimetic covalent bonds, akin to biological muscle tissue, in which isophorone diisocyanate was used as the chemical crosslinking agent. Then, poplar lignin–MCC was mixed with polyacrylonitrile to serve as the precursor for electrospinning. The results show that due to the effective covalent-bond connection, the precursor fibers possess excellent morphology, smooth surface, good thermal stability, and high flexibility and toughness (average elongation-at-break is 51.84%). Therefore, after thermal stabilization and carbonization, derived lignocellulose-based carbon fibers (CFs) with a reduced cost, complete fiber morphology with a uniform diameter (0.48 ± 0.22 μm), and high graphitization degree were obtained. Finally, the electrodes fabrication and electrochemical testing were carried out. The results of electrochemical impedance spectroscopy (EIS) indicate that the Rs and Rct values of CFs supercapacitors are 1.18 Ω and 0.14 Ω, respectively. Results of cyclic voltammetry (CV) and galvanostatic charge–discharge (GCD) suggest that these CFs demonstrate great application potential in electrochemical materials.