Lithium-air batteries are considered to be a potential alternative to lithium-ion batteries for transportation applications, owing to their high theoretical specific energy. So far, however, such systems have been largely restricted to pure oxygen environments (lithium-oxygen batteries) and have a limited cycle life owing to side reactions involving the cathode, anode and electrolyte. In the presence of nitrogen, carbon dioxide and water vapour, these side reactions can become even more complex. Moreover, because of the need to store oxygen, the volumetric energy densities of lithium-oxygen systems may be too small for practical applications. Here we report a system comprising a lithium carbonate-based protected anode, a molybdenum disulfide cathode and an ionic liquid/dimethyl sulfoxide electrolyte that operates as a lithium-air battery in a simulated air atmosphere with a long cycle life of up to 700 cycles. We perform computational studies to provide insight into the operation of the system in this environment. This demonstration of a lithium-oxygen battery with a long cycle life in an air-like atmosphere is an important step towards the development of this field beyond lithium-ion technology, with a possibility to obtain much higher specific energy densities than for conventional lithium-ion batteries.