Aspects of the invention are associated with the discovery of approaches for the conversion of sour natural gas streams, by conversion to liquid hydrocarbons. Particular processes and their associated apparatuses advantageously combine (i) dehydroaromatization (DHA) of methane in a gaseous feedstock, to produce aromatic hydrocarbons such as benzene, with (ii) the reaction of H2S and methane in this feedstock, to produce organic sulfur compounds such as carbon disulfide (CS2) and thiophene (C4H4S). A gaseous product having a reduced concentration of H2S is thereby generated. The aromatic hydrocarbons and organic sulfur compounds may be recovered in a liquid product. Both the gaseous and liquid products may be easily amenable to further upgrading. Other advantages of the disclosed processes and apparatuses reside in their simplicity, whereby the associated streams, including a potential gaseous recycle, generally avoid high partial pressures of H2S.