The electrochemical lithiation and delithiation of the layered oxysulfide Sr₂MnO₂Cu_4-δS₃ has been investigated by using a combination of in situ powder X-ray diffraction and ex situ neutron powder diffraction, X-ray absorption and ⁷Li NMR spectroscopy, together with a range of electrochemical experiments. Sr₂MnO₂Cu_4-δS₃ consists of [Sr₂MnO₂] perovskite-type cationic layers alternating with highly defective antifluorite-type [Cu_4-δS₃] (δ ≈ 0.5) anionic layers. It undergoes a combined displacement/intercalation (CDI) mechanism on reaction with Li, where the inserted Li replaces Cu, forming Li₄S₃ slabs and Cu⁺ is reduced and extruded as metallic particles. For the initial 2-3% of the first discharge process, the vacant sites in the sulfide layer are filled by Li; Cu extrusion then accompanies further insertion of Li. Mn^2.5+ is reduced to Mn²⁺ during the first half of the discharge. The overall charging process involves the removal of Li and re-insertion of Cu into the sulfide layers with re-oxidation of Mn²⁺ to Mn^2.5+. However, due to the different diffusivities of Li and Cu, the processes operating on charge are quite different from those operating during the first discharge: charging to 2.75 V results in the removal of most of the Li, little reinsertion of Cu, and good capacity retention. A charge to 3.75 V is required to fully reinsert Cu, which results in significant changes to the sulfide sublattice during the following discharge and poor capacity retention. This detailed structure-property investigation will promote the design of new functional electrodes with improved device performance.