There is a growing demand for bifunctional electrocatalysts for oxygen electrodes in rechargeable metal-air batteries. This article investigates the bifunctional activity of La single-atom catalysts with N/C coordination (LaNxC6-x@Gra) using density functional theory (DFT). The augmentation of N coordination will result in enhanced synthetic stability. The coordination between nitrogen and carbon (N/C) has a significant influence on the working stability of the system under consideration. In the context of active atoms, the coordination between nitrogen and carbon (N/C coordination) has a significant impact on the electronic structure. This, in turn, influences the adsorption performance and catalytic activity of the catalysts. In the case of stable coordination environments, a correlation exists between the f-orbital center (εf) and the overpotential (η) via the adsorption free energy of intermediates (ΔG*ads). This correlation serves as a useful tool for predicting catalytic performance. The LaNxC6-x@Gra exhibits remarkable bifunctional activity due to its complementary performance, with an overpotential for the oxygen reduction reaction (ηORR) of 0.66 V and an overpotential for the oxygen evolution reaction (ηOER) of 0.43 V. This makes it a promising candidate for use as a bifunctional electrocatalyst in oxygen electrodes.