Past life on Mars will have generated organic remains that may be preserved in present day Mars rocks. The most recent period in the history of Mars that retained widespread surface waters was the late Noachian and early Hesperian and thus possessed the potential to sustain the most evolved and widely distributed martian life. Guidance for investigating late Noachian and early Hesperian rocks is provided by studies of analogous acidic and sulfur-rich environments on Earth. Here we report organic responses for an acid stream containing acidophilic organisms whose post-mortem remains are entombed in iron sulphates and iron oxides. We find that, if life was present in the Hesperian, martian organic records will comprise microbial lipids. Lipids are a potential sizeable reservoir of fossil carbon on Mars, and can be used to distinguish between different domains of life. Concentrations of lipids, and particularly alkanoic or "fatty" acids, are highest in goethite layers that reflect high water-to-rock ratios and thus a greater potential for habitability. Goethite can dehydrate to hematite, which is widespread on Mars. Mars missions should seek to detect fatty acids or their diagenetic products in the oxides and hydroxides of iron associated with sulphur-rich environments.