Exploring new solid-state electrolyte (SSE) materials with good electrochemical stability and high Li-ion conductivity for all-solid-state Li-ion batteries is vital for the development of technologies. Herein, we employ two lithium aluminates, α- and β-Li 5 AlO 4 (α- and β-LAO), as the model framework, which have an orthorhombic crystal structure and isolated AlO 4 tetrahedron units connected in lithium atoms, exhibiting large band gaps, low migration barriers (0.30-0.40 eV), fast Li-ion conductivity (LIC, in a magnitude of 10 -4 S/cm), and a good electrochemical stability window (ESW, [0.01-3.20 V] vs Li + /Li). We tabulate the expected decomposition products at the interface, while considering cathodes in combination with the LAO electrolyte to discuss their compatibility. We also examine the electrochemical stability, H 2 O/CO 2 stability, and Li-ion mobility of Li 4.6 Al 0.6 Si 0.4 O 4 (LASO), Li 5 GaO 4 (LGaO), and Li 4.6 Ga 0.6 Ge 0.4 O 4 (LGaGeO) compounds. In general, there is usually a trade-off between the LIC and the ESW; however, LAO features a good balance between an outstanding LIC and a wide ESW, making the compound a promising candidate for next-generation SSE materials.