With large spin-orbit coupling, the electron configuration in d-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d 5 iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li₂RhO₃, a 4d⁵ honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural 5d⁵ iridate Li₂IrO ₃, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.