The segmentation of COVID-19 lesions from computed tomography (CT) scans is crucial to develop an efficient automated diagnosis system. Deep learning (DL) has shown success in different segmentation tasks. However, an efficient DL approach requires a large amount of accurately annotated data, which is difficult to aggregate owing to the urgent situation of COVID-19. Inaccurate annotation can easily occur without experts, and segmentation performance is substantially worsened by noisy annotations. Therefore, this study presents a reliable and consistent temporal-ensembling (RCTE) framework for semi-supervised lesion segmentation. A segmentation network is integrated into a teacher-student architecture to segment infection regions from a limited number of annotated CT scans and a large number of unannotated CT scans. The network generates reliable and unreliable targets, and to evenly handle these targets potentially degrades performance. To address this, a reliable teacher-student architecture is introduced, where a reliable teacher network is the exponential moving average (EMA) of a reliable student network that is reliably renovated by restraining the student involvement to EMA when its loss is larger. We also present a noise-aware loss based on improvements to generalized cross-entropy loss to lead the segmentation performance toward noisy annotations. Comprehensive analysis validates the robustness of RCTE over recent cutting-edge semi-supervised segmentation techniques, with a 65.87% Dice score.