The overturn of titanium-rich mantle cumulates has been invoked to explain the structure and dynamics of the Moon. These dense cumulates are stable at the core-mantle boundary (CMB) and could explain field observations inferred from geophysical studies. We report acoustic and electrical experiments on natural ilmenite-rutile aggregates up to 4.5 GPa and 1920 K. Seismic velocities show a weak pressure and temperature dependence, with Vs similar to 4.2 (+/-0.2) km/s and Vp similar to 8.0 (+/-0.2) km/s at the CMB conditions. Conductivity increases by a factor of 10(4) from 373 to 1920 K and is >10(3) S/m above 1573 K. Seismic and electrical models for the lunar mantle based on our results, considering mixtures of Fe-Ti oxides and olivine, indicate that field velocity and conductivity estimates are reproduced satisfactorily with 3-16 vol.% Fe-Ti oxides and 20 vol.% melt. Interactions between a Ti-rich, melt-bearing layer and the adjacent core likely affect the cooling and magnetic history of the Moon.