Accurate coronary lumen segmentation on coronary-computed tomography angiography (CCTA) images is crucial for quantification of coronary stenosis and the subsequent computation of fractional flow reserve. Many factors including difficulty in labeling coronary lumens, various morphologies in stenotic lesions, thin structures and small volume ratio with respect to the imaging field complicate the task. In this work, we fused the continuity topological information of centerlines which are easily accessible, and proposed a novel weakly supervised model, Examinee-Examiner Network (EE-Net), to overcome the challenges in automatic coronary lumen segmentation. First, the EE-Net was proposed to address the fracture in segmentation caused by stenoses by combining the semantic features of lumens and the geometric constraints of continuous topology obtained from the centerlines. Then, a Centerline Gaussian Mask Module was proposed to deal with the insensitiveness of the network to the centerlines. Subsequently, a weakly supervised learning strategy, Examinee-Examiner Learning, was proposed to handle the weakly supervised situation with few lumen labels by using our EE-Net to guide and constrain the segmentation with customized prior conditions. Finally, a general network layer, Drop Output Layer, was proposed to adapt to the class imbalance by dropping well-segmented regions and weights the classes dynamically. Extensive experiments on two different data sets demonstrated that our EE-Net has good continuity and generalization ability on coronary lumen segmentation task compared with several widely used CNNs such as 3D-UNet. The results revealed our EE-Net with great potential for achieving accurate coronary lumen segmentation in patients with coronary artery disease. Code at http://github.com/qiyaolei/Examinee-Examiner-Network.