The roles of lithium aluminum germanium phosphate (LAGP) glass-ceramic (GC) in cathodes of totally solid-state lithium-oxygen (Li-O-2) electrochemical cells are delineated by conducting discharge experiments as a function of cathode chemistry. It is proposed that LAGP possesses an inherent characteristic to adsorb oxygen molecules due to its open structure. The adsorption is followed by reduction of oxygen to superoxide and peroxide molecules. Subsequently, these molecules react with lithium ions to form respective discharge products. In addition to being an important constituent of the cathode, the LAGP also serves as a solid-state electrolyte membrane due to its superionic lithium-ion conductivity. The dual functions of the LAGP GCs make it a feasible material to process an integrated membrane-cathode element of a Li-O-2 cell, although this is not demonstrated in this paper.