Advances in technology have facilitated the development of lightning research and data processing. The electromagnetic pulse signals emitted by lightning (LEMP) can be collected by very low frequency (VLF)/low frequency (LF) instruments in real time. The storage and transmission of the obtained data is a crucial link, and a good compression method can improve the efficiency of this process. In this paper, a lightning convolutional stack autoencoder (LCSAE) model for compressing LEMP data was designed, which converts the data into low-dimensional feature vectors through the encoder part and reconstructs the waveform through the decoder part. Finally, we investigated the compression performance of the LCSAE model for LEMP waveform data under different compression ratios. The results show that the compression performance is positively correlated with the minimum feature of the neural network extraction model. When the compressed minimum feature is 64, the average coefficient of determination $R^2$ of the reconstructed waveform and the original waveform can reach 96.7%. It can effectively solve the problem regarding the compression of LEMP signals collected by the lightning sensor and improve the efficiency of remote data transmission.