We report a new fast ion-conducting lithium thioborate halide, Li6B7S13I, that crystallizes in either a cubic or tetragonal thioboracite structure, which is unprecedented in boron-sulfur chemistry. The cubic phase exhibits a perovskite topology and an argyrodite-like lithium substructure that leads to superionic conduction with a theoretical Li-ion conductivity of 5.2 mS cm-1 calculated from ab initio molecular dynamics (AIMD). Combined single-crystal X-ray diffraction, neutron powder diffraction, and AIMD simulations elucidate the Li+-ion conduction pathways through 3D intra- and intercage connections and Li-ion site disorder, which are all essential for high lithium mobility. Furthermore, we demonstrate that Li+ ordering in the tetragonal polymorph impedes lithium-ion conduction, thus highlighting the importance of the lithium substructure and lattice symmetry in dictating transport properties.