Aortic dissection is defined as a separation of layers of the aortic wall leading high mortality. Accurately segmenting both the true and false lumens is critical for revealing geometrical characteristics for diagnosis and evaluation of the dissection. Existing aortic dissection segmentation methods are mainly convolutional neural network (CNN)-based and are limited in precisely distinguishing these lumens due to lack of long-range dependencies along the aorta. To address this issue, we propose an integrated CNN and transformer prediction network (ICTP-Net) to capture both low-level spatial details and long-range global dependencies. Rather than a simple concatenation and fusion, an attention fusion (AF) block is employed to merge features from two branches. Additionally, due to the vascular anatomy, the proposed network is trained and applied in a sliding-context-dependent manner where we use partial previous segmentation for the prediction of the next section, further enhancing the spatial continuity along the aorta. 726 data samples were used in the experiments, and comparative and ablation studies show that the proposed ICTP-Net achieves the best aortic dissection true lumen segmentation compared with other state-of-the-art methods, demonstrating the effectiveness of the model integration, AF module and the sliding-context-dependent design.