Graphyne, which contains planar sheets equally occupied by sp(2) and sp carbon atoms, is a layered carbon allotrope. Since the length of the acetylene chains within graphyne can be variable by adjusting the number of acetylenic linkages (-C C-) between carbon hexagons, resulting in a family of graphyne-extended graphynes (i. e. graph-n-ynes). In this work, density functional theory (DFT) calculations were carried out to investigate the adsorption of lithium atoms on extended graphynes monolayers, and the results were compared to extrapolate the potential relationship between lithium storage capacity and the number of acetylenic linkages. The results show that further extending the acetylenic chains might not be helpful in achieving higher capacity. The longer acetylene chains result in the lower carbon atom density, as well as the lower stability of the carbon networks, which should be taken into consideration seriously. High-capacity Li storage as LiC3 in graphdiyne and graph-5-yne, was achieved, and the preferred adsorption sites for Li were identified computationally. With high Li storage capacity and structural advantages, these porous carbon materials are expected to be applied in efficient lithium storage.