Power fault monitoring based on acoustic waves has gained a great deal of attention in industry. Existing methods for fault diagnosis typically collect sound signals on site and transmit them to a back-end server for analysis, which may fail to provide a real-time response due to transmission packet loss and latency. However, the limited computing power of edge devices and the existing methods for feature extraction pose a significant challenge to performing diagnosis on the edge. In this paper, we propose a fast Lightweight Fault Diagnosis method for power transformers, referred to as LightFD, which integrates several technical components. Firstly, before feature extraction, we design an asymmetric Hamming-cosine window function to reduce signal spectrum leakage and ensure data integrity. Secondly, we design a multidimensional spatio-temporal feature extraction method to extract acoustic features. Finally, we design a parallel dual-layer, dual-channel lightweight neural network to realize the classification of different fault types on edge devices with limited computing power. Extensive simulation and experimental results show that the diagnostic precision and recall of LightFD reach 94.64% and 95.33%, which represent an improvement of 4% and 1.6% over the traditional SVM method, respectively.