The present-day interior structure of the Moon is thought to consist of an iron-rich core, overlain with a silicate mantle (e.g., olivine, pyroxene, and garnet), beneath a plagioclase crust. However, despite the increasing number of direct geophysical observables that are becoming available, many aspects of the lunar interior structure and mineralogy remain largely unconstrained. A central question arises from observations relating to the deep lunar interior, which have identified a distinct feature above the core-mantle boundary at ~1200 km depth; characterised by its high densities and low seismic velocities, this may be interpreted as a partial melt layer. The origin of this layer could stem from much shallower depths, where Ti-rich material may have sunk due to its gravitational instability. Should Ti-rich material have accumulated at the core-mantle boundary, and undergone partial melting, the resultant Ti-rich liquids may remain stable to the present-day. The fate of these liquids is, however, highly dependent on their composition, and determined by their buoyancy and mobility within the lunar mantle. In this work we present the densities of Ti-rich liquids of relevance to the lunar interior, determined via high-pressure high-temperature in situ density measurements using the X-ray absorption method in a Paris-Edinburgh press. We apply our results within the context of their buoyancy within the lunar mantle, and their implications for the evolution and present-day structure of the lunar interior.