In order to understand the structural and compositional factors controlling lithium transport in sulfides, we explored the Li5AlS4 – Li4GeS4 phase field for new materials. Both parent compounds are defined structurally by a hexagonal close packed sulfide lattice, where distinct arrangements of tetrahedral metal sites give Li5AlS4 a layered structure and Li4GeS4 a three dimensional structure related to γ-Li3PO4. The combination of the two distinct structural motifs is expected to lead to new structural chemistry. We identified the new crystalline phase Li4.4Al0.4Ge0.6S4, and investigated the structure and Li+ ion dynamics of the family of structurally related materials Li4.4M0.4M’0.6S4 (M= Al3+, Ga3+ and M’= Ge4+, Sn4+). We used neutron diffraction to solve the full structures of the Al-homologues, which adopt a layered close-packed structure with a new arrangement of tetrahedral (M/M’) sites and a novel combination of ordered and disordered lithium vacancies. AC impedance spectroscopy revealed lithium conductivities in the range 3(2) x 10-6 to 4.3(3) x 10-5 S cm-1 at room temperature with activation energies between 0.43(1) and 0.38(1) eV. Electrochemical performance was tested in a plating and stripping experiment against Li metal electrodes and showed good stability of the Li4.4Al0.4Ge0.6S4 phase over 200 hours. A combination of variable temperature 7Li solid state nuclear magnetic resonance spectroscopy and ab initio molecular dynamics calculations on selected phases showed that two dimensional diffusion with a low energy barrier of 0.17 eV is responsible for long-range lithium transport, with diffusion pathways mediated by the disordered vacancies while the ordered vacancies do not contribute to the conductivity. This new structural family of sulfide Li+ ion conductors offers insight into the role of disordered vacancies on Li+ ion conductivity mechanisms in hexagonally close packed sulfides that can inform future materials design.