Nearly all high–energy density cathodes for rechargeable lithium batteries are well-ordered materials in which lithium and other cations occupy distinct sites. Cation-disordered materials are generally disregarded as cathodes because lithium diffusion tends to be limited by their structures. The performance of Li$_{1.211}$Mo$_{0.467}$Cr$_{0.3O2}$ shows that lithium diffusion can be facile in disordered materials. Using ab initio computations, we demonstrate that this unexpected behavior is due to percolation of a certain type of active diffusion channels in disordered Li-excess materials. A unified understanding of high performance in both layered and Li-excess materials may enable the design of disordered-electrode materials with high capacity and high energy density.