Experimental evidence has demonstrated that the presence of water in non-aqueous electrolytes significantly affects Li-O2 electrochemistry. Understanding the reaction mechanism for Li2O2 formation in the presence of water impurities is important to understand Li-O2 battery performance. A recent experiment has found that very small amounts of water (as low as 40 ppm) can significantly affect the product formation in Li-O2 batteries as opposed to essentially no water (1 ppm). Although experimental as well as theoretical work has proposed mechanisms of Li2O2 formation in the presence of much larger amounts of water, none of the mechanisms provide an explanation for the observations for very small amounts of water. In this work, density functional theory (DFT) was utilized to obtain a mechanistic understanding of the Li-O2 discharge chemistry in a dimethoxyethane (DME) electrolyte containing an isolated water and no water. The reaction pathways for Li2O2 formation from LiO2 on a model system were carefully evaluated with different level of theories, i.e. PBE (PW), B3LYP/6-31G(2df,p), B3LYP/6-311++G(2df,p) and G4MP2. The results indicate that the LiO2 disproportionation reaction to Li2O2 can be promoted by the water in DME electrolyte, which explains why there is a significant difference compared to when no water is present in the experimentally observed discharge product distributions. Ab initio molecular dynamics calculations were also used to investigate the disproportionation of LiO2 dimer in explicit DME. This work adds to the fundamental understanding of the discharge chemistry of a Li-O2 battery.