Fall accidents in industrial and construction environments require an immediate reaction, to provide first aid. Shortening the time between the fall and the relevant personnel being notified can significantly improve the safety and health of workers. Therefore, in this work, an IoT system for real-time fall detection is proposed, using the ASSIST-IoT reference architecture. Empowered with a machine learning model, the system can detect fall accidents and swiftly notify the occupational health and safety manager. To train the model, a novel multimodal fall detection dataset was collected from ten human participants and an anthropomorphic dummy, covering multiple types of fall, including falls from a height. The dataset includes absolute location and acceleration measurements from several IoT devices. Furthermore, a lightweight long short-term memory model is proposed for fall detection, capable of operating in an IoT environment with limited network bandwidth and hardware resources. The accuracy and F1-score of the model on the collected dataset were shown to exceed 0.95 and 0.9, respectively. The collected multimodal dataset was published under an open license, to facilitate future research on fall detection methods in occupational health and safety.