Terrain mapping has a many use cases in both land surveyance and autonomous vehicles. Popular methods generate occupancy maps over 3D space, which are sub-optimal in outdoor scenarios with large, clear spaces where gaps in LiDAR readings are common. A terrain can instead be modelled as a height map over 2D space which can iteratively be updated with incoming LiDAR data, which simplifies computation and allows missing points to be estimated based on the current terrain estimate. The latter point is of particular interest, since it can reduce the data collection effort required (and its associated costs) and current options are not suitable to real-time operation. In this work, we introduce a new method that is capable of performing such terrain mapping and inferencing tasks in real-time. We evaluate it with a set of mapping scenarios and show it is capable of generating maps with higher accuracy than an OctoMap-based method.