Log anomaly detection on edge devices is the key to enhance edge security when deploying IoT systems. Despite the success of many newly proposed deep learning based log anomaly detection methods, handling large-scale logs on edge devices is still a bottleneck due to the limited computational power on these devices to fulfil the real-time processing requirement for accurate anomaly detection. In this work, we propose a novel lightweight log anomaly detection algorithm, named LightLog, to tackle this research gap. In specific, we achieve real-time processing speed on the task via two aspects: (i) creation of a low-dimensional semantic vector space based on word2vec and post-processing algorithms (PPA); and (ii) design of a lightweight temporal convolutional network (TCN) for the detection. These two components significantly reduce the number of parameters and computations of a standard TCN while improving the detection performance. Experimental results show that our LightLog outperforms several benchmarking methods, namely DeepLog, LogAnomaly and RobustLog, by achieving 97.0 F1 score on HDFS Dataset and 97.2 F1 score on BGL with smallest model size. This effective yet efficient method paves the way to the deployment of log anomaly detection on the edge. Our source code and datasets are freely available on https://github.com/Aquariuaa/LightLog.