Objective. Deep learning (DL) methods have been widely utilized in ultrasound (US) image segmentation tasks. However, current DL segmentation methods for US images are typically developed only for lesion segmentation of specific organs; e.g. breast or thyroid US. So far, there is currently no general-purpose lesion segmentation framework for US images that can be implemented across various organs in computer aided diagnosis scenarios. Considering that most lesion locations in US images have abnormal ultrasonic echo intensities or patterns that may be visually distinct from surrounding normal tissues or organs, it is thus possible to develop a universal lesion segmentation framework for US images (named as ULS4US), focusing on effectively identifying and segmenting lesions of various sizes in different organs. Approach. The proposed ULS4US framework comprises three components: (1) a multiple-in multi-out (MIMO) UNet that incorporates multiscale features extracted from the US image and lesion, (2) a novel two-stage lesion-aware learning algorithm that recursively locates and segments the lesions in a reinforced manner, and (3) a lesion-adaptive loss function for the MIMO-UNet that integrates two weighted components and one self-supervised component designed for intra- and inter-branches of network outputs, respectively. Main Results. Compared to six state-of-the-art segmentation models, ULS4US has achieved superior performance (accuracy of 0.956, DSC of 0.836, HD of 7.849, and mIoU of 0.731) in a unified dataset consisting of two public and three private US image datasets, which include over 2200 images of three specific types of organs. Comparative experiments on both individual and unified datasets suggest that ULS4US is likely scalable with additional data. Significance. The study demonstrates the potential of DL-based universal lesion segmentation approaches in clinical US, which would substantially reduce clinician workload and enhance diagnostic accuracy.