Hydrogen sulphide (H2S) is toxic and can act as a selective pressure on aquatic organisms, facilitating a wide range of adaptations for life in sulphidic environments. Mangrove rivulus (Kryptolebias marmoratus) inhabit mangrove swamps and have developed high tolerance to environmental H2S. They are hermaphroditic and can self-fertilize, producing distinct isogenic lineages with different sensitivity to H2S. Here, we tested the hypothesis that observed differences in responses to H2S are the result of differences in mitochondrial functions. For this purpose, we performed two experimental series, testing (1) the overall mitochondrial oxidizing capacities and (2) the kinetics of apparent H2S mitochondrial oxidation and inhibition in two distinct lineages of mangrove rivulus, originally collected from Belize and Honduras. We used permeabilized livers from both lineages, measured mitochondrial oxidation, and monitored changes during gradual increases of sulphide. Ultimately, we determined that each lineage has a distinct strategy for coping with elevated H2S, indicating divergences in mitochondrial function and metabolism. The Honduras lineage has higher anaerobic capacity substantiated by higher lactate dehydrogenase activity and higher apparent H2S oxidation rates, likely enabling them to tolerate H2S by escaping aquatic H2S in a terrestrial environment. However, Belize fish have increased cytochrome c oxidase and citrate synthase activities as well as increased succinate contribution to mitochondrial respiration, allowing them to tolerate higher levels of aquatic H2S without inhibition of mitochondrial oxygen consumption. Our study reveals distinct physiological strategies in genetic lineages of a single species, indicating possible genetic and/or functional adaptations to sulphidic environments at the mitochondrial level.