Very recently a quantum liquid was reported to form in H3LiIr2O6, an iridate proposed to be a close realization of the Kitaev honeycomb model. To test this assertion we perform detailed quantum chemistry calculations to determine the magnetic interactions between Ir moments. We find that weakly bond dependent ferromagnetic Kitaev exchange dominates over other couplings, but still is substantially lower than in Na2IrO3. This reduction is caused by the peculiar position of the interlayer species: removing hydrogen cations next to a Ir2O2 plaquette increases the Kitaev exchange by more than a factor of 3 on the corresponding Ir-Ir link. Consequently, any lack of hydrogen order will have a drastic effect on the magnetic interactions and strongly promote spin disordering.