Lucus Planum, extending for a radius of approximately 500km around 181 degrees E, 5 degrees S, is part of the Medusae Fossae Formation (MFF), a set of several discontinuous deposits of fine-grained, friable material straddling across the Martian highland-lowland boundary. The MFF has been variously hypothesized to consist of pyroclastic flows, pyroclastic airfall, paleopolar deposits, or atmospherically deposited icy dust driven by climate cycles. Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS), a low-frequency subsurface-sounding radar carried by European Space Agency's Mars Express, acquired 238 radar swaths across Lucus Planum, providing sufficient coverage for the study of its internal structure and dielectric properties. Subsurface reflections were found only in three areas, marked by a distinctive surface morphology, while the central part of Lucus Planum appears to be made of radar-attenuating material preventing the detection of basal echoes. The bulk dielectric properties of these areas were estimated and compared with those of volcanic rocks and ice-dust mixtures. Previous interpretations that east Lucus Planum and the deposits on the northwestern flanks of Apollinaris Patera consist of high-porosity pyroclastic material are strongly supported by the new results. The northwestern part of Lucus Planum is likely to be much less porous, although interpretations about the nature of the subsurface materials are not conclusive. The exact origin of the deposits cannot be constrained by radar data alone, but our results for east Lucus Planum are consistent with an overall pyroclastic origin, likely linked to Tharsis Hesperian and Amazonian activity. Plain Language Summary Lobe-shaped thick deposits, collectively known as the Medusae Fossae Formation, are found west of the Olympus Mons volcano on Mars. Visual observations of these smooth and relatively unremarkably looking materials have not definitively determined how they formed with hypotheses ranging from volcanic ash to remnants of a materials deposited at a previous location of the north pole, to accumulation of atmospheric dust. In this study we used the ground penetrating radar on board Mars Express to see through these deposits to derive information about Lucus Planum, the central lobe of the Medusae Fossae Formation. Through our analysis of the way the radar waves were reflected by subsurface layering, we concluded that the materials forming Lucus Planum are spatially variable: the east and west portions of the deposits are highly porous and probably composed of ashes and rocks from nearby volcanoes. In the north-west the deposits are much denser, but we could not unequivocally define their nature. Finally, our instrument could not detect signals from the central part of Lucus Planum, which suggests yet a different component in the deposits. This diversity points to a dynamic geological history in this unique region of Mars.