The utilization of Very Low Frequency (VLF) electromagnetic signals in navigation systems is widespread. However, the non-stationary behavior of lightning signals can affect VLF electromagnetic signal transmission. Accurately classifying lightning signals is important for reducing interference and noise in VLF, thereby improving the reliability and overall performance of navigation systems. In recent years, the evolution of deep learning, specifically Convolutional Neural Network (CNNs), has sparked a transformation in lightning classification, surpassing traditional statistical methodologies. Existing CNN models have limitations as they overlook the diverse attributes of lightning signals across different scales and neglect the significance of temporal sequencing in sequential signals. This study introduces an innovative multi-scale residual transform (MRTransformer) that not only has the ability to discern intricate fine-grained patterns while also weighing the significance of different aspects within the input lightning signal sequence. This model performs the attributes of the lightning signal across different scales and the level of accuracy reached 90% in the classification. In future work, this model has the potential applied to a comprehensive understanding of the localization and waveform characteristics of lightning signals.