Aerosols are significant to the Earth's climate, with nearly all atmospheric aerosols containing organic compounds that often contain both hydrophilic and hydrophobic parts. However, the nature of how these compounds are arranged within an aerosol droplet remains unknown. Here we demonstrate that fatty acids in proxies for atmospheric aerosols self-assemble into highly ordered three-dimensional nanostructures that may have implications for environmentally important processes. Acoustically trapped droplets of oleic acid/sodium oleate mixtures in sodium chloride solution are analysed by simultaneous synchrotron small-angle X-ray scattering and Raman spectroscopy in a controlled gas-phase environment. We demonstrate that the droplets contained crystal-like lyotropic phases including hexagonal and cubic close-packed arrangements of spherical and cylindrical micelles, and stacks of bilayers, whose structures responded to atmospherically relevant humidity changes and chemical reactions. Further experiments show that self-assembly reduces the rate of the reaction of the fatty acid with ozone, and that lyotropic-phase formation also occurs in more complex mixtures more closely resembling compositions of atmospheric aerosols. We suggest that lyotropic-phase formation likely occurs in the atmosphere, with potential implications for radiative forcing, residence times and other aerosol characteristics.