Lithium-titanium-sulfur cathodes have garnered interest due to their distinctive properties and potential applications in lithium-ion batteries. They present various benefits, including lower cost, enhanced safety, and greater energy density compared to the commonly used transition metal oxides. The current trend in lithium-ion batteries is to move to all-solid-state chemistries in order to improve safety and energy density. Several chemistries for solid electrolytes have been studied, tested, and characterized to evaluate the applicability in energy storage system. Among those, sulfur-based Argyrodites have been coupled with cubic rock-salt type Li2TiS3 electrodes. In this work, Li2TiS3 surfaces were investigated with DFT methods in different conditions, covering the possible configurations that can occur during the cathode usage: pristine, delithiated, and overlithiated. Interfaces were built by coupling selected Li2TiS3 surfaces with the most stable Argyrodite surface, as derived from a previous study, allowing us to understand the (electro)chemical compatibility between these two sulfur-based materials.