The framework materials Li3Fe(MoO4)3 and Li1.6Mn2.2(MoO4)3 contain networks of Fe/MnO6 and MoO4 units. These compounds are similar structures to the recently reported cathode material Li3Cr(MoO4)3 showing exceptional lithium storage based on redox activity of Mo in addition to the transition metal. We have found exceptionally high Li+ conductivity in the title phases. The structures of these materials have been determined previously using X-ray scattering, which is notoriously unreliable in detecting the subtle interstitial sites and disorder often associated with lithium mobility in solids. Neutron diffraction will give an accurate assessment of the lithium distribution in these compounds, and so reveal the origin of the facile Li+ migration through the structure. The chemical flexibility of these materials suggests battery cathode and electrolyte can share framework structures.