Shadow removal can significantly improve the image visual quality and has many applications in computer vision. Deep learning methods based on CNNs have become the most effective approach for shadow removal by training on either paired data, where both the shadow and underlying shadow-free versions of an image are known, or unpaired data, where shadow and shadow-free training images are totally different with no correspondence. In practice, CNN training on unpaired data is more preferred given the easiness of training data collection. In this paper, we present a new Lightness-Guided Shadow Removal Network (LG-ShadowNet) for shadow removal by training on unpaired data. In this method, we first train a CNN module to compensate for the lightness and then train a second CNN module with the guidance of lightness information from the first CNN module for final shadow removal. We also introduce a loss function to further utilise the colour prior of existing data. Extensive experiments on widely used ISTD, adjusted ISTD and USR datasets demonstrate that the proposed method outperforms the state-of-the-art methods with training on unpaired data.