The novel Coronavirus disease (COVID-19) is a highly contagious virus and has spread all over the world, posing an extremely serious threat to all countries. Automatic lung infection segmentation from computed tomography (CT) plays an important role in the quantitative analysis of COVID-19. However, the major challenge lies in the inadequacy of annotated COVID-19 datasets. Currently, there are several public non-COVID lung lesion segmentation datasets, providing the potential for generalizing useful information to the related COVID-19 segmentation task. In this paper, we propose a novel relation-driven collaborative learning model to exploit shared knowledge from non-COVID lesions for annotation-efficient COVID-19 CT lung infection segmentation. The model consists of a general encoder to capture general lung lesion features based on multiple non-COVID lesions, and a target encoder to focus on task-specific features based on COVID-19 infections. Features extracted from the two parallel encoders are concatenated for the subsequent decoder part. We develop a collaborative learning scheme to regularize feature-level relation consistency of given input and encourage the model to learn more general and discriminative representation of COVID-19 infections. Extensive experiments demonstrate that trained with limited COVID-19 data, exploiting shared knowledge from non-COVID lesions can further improve state-of-the-art performance with up to 3.0% in dice similarity coefficient and 4.2% in normalized surface dice. Our proposed method promotes new insights into annotation-efficient deep learning for COVID-19 infection segmentation and illustrates strong potential for real-world applications in the global fight against COVID-19 in the absence of sufficient high-quality annotations.