Understanding the spreading of molten core materials (corium) is vital for achieving post-accident heat removal and maintaining the integrity of the reactor containment during a severe nuclear accident. The spreading of highly viscous corium over sacrificial concrete and ablation-resistant ceramic substrates, consistent with recent VE-U9 experiments at the VULCANO facility, is investigated using a Lagrangian moving particle hydrodynamics (MPH) method. The spreading dynamics are coupled with a heat transfer model to account for the increase in melt viscosity due to solidification. Three alternative boundary conditions are considered at the melt-substrate interface to mimic the influence of low viscosity concrete ablation products on the spreading dynamics. Simulation of spreading under no-slip conditions closely resembled the spreading behavior observed over the inert ceramic substrate, advancing with a crawling motion with a steep profile in the proximity of the melt front. Spreading terminated due to a combination of thermal radiation from the free surface and the heat transfer to the substrate, leading to the formation of a continuous crust. Introduction of slip boundary models, to mimic lubrication of the interface by a film of low-viscosity concrete decomposition products, enabled the prediction of the gliding flow observed over the sacrificial concrete substrate, characterized by a shallow melt topology near the spreading front. The simulation results demonstrate excellent potential for Lagrangian models such as MPH to predict complex spreading dynamics in the presence of both melt solidification and lubrication at the substrate.