In contrast to accurate GPS-based localization, approaches to localize within LoRaWAN networks offer the advantages of being low power and low cost. This targets a very different set of use cases and applications on the market where accuracy is not the main considered metric. The localization is performed by the Time Difference of Arrival (TDoA) method and provides discrete position estimates on a map. An accurate “tracking-on-demand” mode for retrieving lost and stolen assets is important. To enable this mode, we propose deploying an e-compass in the mobile LoRa node, which frequently communicates directional information via the payload of the LoRaWAN uplink messages. Fusing this additional information with raw TDoA estimates in a map matching algorithm enables us to estimate the node location with a much increased accuracy. It is shown that this sensor fusion technique outperforms raw TDoA at the cost of only embedding a low-cost e-compass. For driving, cycling, and walking trajectories, we obtained minimal improvements of 65, 76, and 82% on the median errors which were reduced from 206 to 68 m, 197 to 47 m, and 175 to 31 m, respectively. The energy impact of adding an e-compass is limited: energy consumption increases by only 10% compared to traditional LoRa localization, resulting in a solution that is still 14 times more energy-efficient than a GPS-over-LoRa solution.