Lesion segmentation in medical imaging serves as an effective tool for assessing tumor sizes and monitoring changes in growth. However, not only is manual lesion segmentation time-consuming, but it is also expensive and requires expert radiologist knowledge. Therefore many hospitals rely on a loose substitute called response evaluation criteria in solid tumors (RECIST). Although these annotations are far from precise, they are widely used throughout hospitals and are found in their picture archiving and communication systems (PACS). Therefore, these annotations have the potential to serve as a robust yet challenging means of weak supervision for training full lesion segmentation models. In this work, we propose a weakly-supervised co-segmentation model that first generates pseudo-masks from the RECIST slices and uses these as training labels for an attention-based convolutional neural network capable of segmenting common lesions from a pair of CT scans. To validate and test the model, we utilize the DeepLesion dataset, an extensive CT-scan lesion dataset that contains 32,735 PACS bookmarked images. Extensive experimental results demonstrate the efficacy of our co-segmentation approach for lesion segmentation with a mean Dice coefficient of 90.3%.