Lesion segmentation on computed tomography (CT) scans is an important step for precisely monitoring changes in lesion/tumor growth. This task, however, is very challenging since manual segmentation is prohibitively timeconsuming, expensive, and requires professional knowledge. Current practices rely on an imprecise substitute called response evaluation criteria in solid tumors (RECIST). Although these markers lack detailed information about the lesion regions, they are commonly found in hospitals’ picture archiving and communication systems (PACS). Thus, these markers have the potential to serve as a powerful source of weak-supervision for 2D lesion segmentation. To approach this problem, this paper proposes a convolutional neural network (CNN) based weakly-supervised lesion segmentation method, which first generates the initial lesion masks from the RECIST measurements and then utilizes co-segmentation to leverage lesion similarities and refine the initial masks. In this work, an attention-based co-segmentation model is adopted due to its ability to learn more discriminative features from a pair of images. Experimental results on the NIH DeepLesion dataset demonstrate that the proposed co-segmentation approach significantly improves lesion segmentation performance, e.g the Dice score increases about 4.0% (from 85.8% to 89.8%).