Radar echo extrapolation is widely used in tasks such as precipitation forecasting and meteorological disaster warning. In recent years, temporal prediction models combined with deep learning have effectively improved forecasting performance. However, several challenges still remain, including insufficient global dependency modeling and blurred forecast images. To improve prediction accuracy, this study proposes a radar echo extrapolation model, DMLSTM, which integrates dynamic window attention memory (DM) with long short-term memory (LSTM) networks. First, dynamic dual-scale window attention is applied to accurately capture multi-scale meteorological structures. Meanwhile, a memory-enhanced sliding window is employed to maintain continuous spatiotemporal evolution. Subsequently, an adaptive residual gating unit suppresses long-range feature attenuation and enhances responsiveness to sudden changes. Finally, a gradient-aligned multi-scale attention loss function is introduced to preserve the physical motion constraints of key meteorological structures. Experimental results indicate that, on the Shenzhen radar echo dataset, compared with the best baseline model (SwinLSTM-B), the proposed model slightly increases the number of parameters. After structural optimization, the single-round inference time increases by 5%, while the mean squared error (MSE) decreases by 10.3% and the structural similarity (SSIM) increases by 1.4%. On the Moving MNIST dataset, the MSE is reduced by 14.9% and the SSIM reaches 0.926. These experimental results demonstrate the advanced performance and strong generalization capability of the proposed model in radar echo extrapolation tasks.