Two lignin-based composite films were prepared by solution casting, which were named Cu-CLA/PVA and CuO-LA/PVA/CNF, respectively. The kinetic and thermodynamic analyses of the deodorization process of the composite membranes were performed by using adsorption models. The results showed that both membranes had good adsorption performance for H2S with the adsorption amounts of 36.39 mg g−1 and 35.69 mg g−1, respectively. The adsorption processes were mainly following the pseudo-secondary kinetic model, intraparticle diffusion model, and Freundlich isothermal adsorption model, indicating that the intraparticle diffusion resistance controlled the H2S adsorption rate and H2S was adsorbed on the non-homogeneous surface of the membranes through multiple layers. The adsorption of H2S by Cu-CLA/PVA is an exothermic process, while the adsorption of H2S by CuO-LA/PVA/CNF is a heat-absorbing process, indicating that Cu-CLA/PVA is more suitable for H2S adsorption at low temperatures, but CuO-LA/PVA/CNF, at higher temperatures, is favorable for H2S adsorption reactions. △G is negative of both Cu-CLA/PVA and CuO-LA/PVA/CNF, indicating that both Cu-CLA/PVA and CuO-LA/PVA/CNF are spontaneous for H2S adsorption.