Since the tumor moves with the patient's breathing movement in clinical surgery, the real-time prediction of respiratory movement is required to improve the efficacy of radiotherapy. Some RNN-based respiratory management methods have been proposed for this purpose. However, these existing RNN-based methods often suffer from the degradation of generalization performance for a long-term window (such as 600 ms) because of the structural consistency constraints. In this paper, we propose an innovative Long Short-term Transformer (LSTformer) for long-term real-time accurate respiratory prediction. Specifically, a novel Long-term Information Enhancement module (LIE) is proposed to solve the performance degradation under a long window by increasing the long-term memory of latent variables. A lightweight Transformer Encoder (LTE) is proposed to satisfy the real-time requirement via simplifying the architecture and limiting the number of layers. In addition, we propose an application-oriented data augmentation strategy to generalize our LSTformer to practical application scenarios, especially robotic radiotherapy. Extensive experiments on our augmented dataset and publicly available dataset demonstrate the state-of-the-art performance of our method on the premise of satisfying the real-time demand.