All-solid electrolytes could lead to a technological breakthrough in the performance of all-solid-state batteries when combined with a lithium-metal anode. However, the use of a lithium-metal anode presents several challenges, such as dendrite growth, interface electrochemical stability, formation and propagation of cracks, and delamination of the electrode/electrolyte interfaces. This work aims to explore the effectiveness of using newly synthesized 2D graphyne-based membranes (namely graphyne, graphdiyne, and graphtriyne) for electrode protection in a solid polymer electrolyte battery through first-principle calculations, nudged elastic band method, and classical molecular dynamics simulation. Specifically, we aim to investigate the effectiveness of these membranes in mitigating the aforementioned challenges. A high external electric field of up to 0.5 V/Å, 0.75 V/Å, and 1 V/Å was applied to accelerate the ions diffusion process. The adsorption energies, charge transfer, and in-plane/out-plane diffusion of single lithium on graphyne-based surfaces were investigated. Afterward, we calculated and compared the Li⁺ permeability, the electrolyte molecules’ rejection efficiency, and the intrinsic properties of graphyne-based nanoporous membranes. Our findings show that both graphyne and graphdiyne surfaces effectively permit Li⁺ intercalation while preventing other electrolyte molecules from reaching the electrodes.