Due to a unique imaging mechanism, Synthetic Aperture Radar (SAR) images typically exhibit degradation phenomena. To enhance image quality and support real-time on-board processing capabilities, we propose a lightweight deep generative network framework, namely, the Lightweight Super-Resolution Generative Adversarial Network (LSRGAN). This method introduces Depthwise Separable Convolution (DSConv) in residual blocks to compress the original Generative Adversarial Network (GAN) and uses the SeLU activation function to construct a lightweight residual module (LRM) suitable for SAR image characteristics. Furthermore, we combine the LRM with an optimized Coordinated Attention (CA) module, enhancing the lightweight network’s capability to learn feature representations. Experimental results on spaceborne SAR images demonstrate that compared to other deep generative networks focused on SAR image super-resolution reconstruction, LSRGAN achieves compression ratios of $74.68\%$ in model storage requirements and $55.93\%$ in computational resource demands. In this work, we significantly reduce the model complexity, improve the quality of spaceborne SAR images, and validate the effectiveness of the SAR image super-resolution algorithm as well as the feasibility of real-time on-board processing technology.