For several skin conditions such as vitiligo, accurate segmentation of lesions from skin images is the primary measure of disease progression and severity. Existing methods for vitiligo lesion segmentation require manual intervention. Unfortunately, manual segmentation is time and labor-intensive, as well as irreproducible between physicians. We introduce a convolutional neural network (CNN) that quickly and robustly performs vitiligo skin lesion segmentation. Our CNN has a U-Net architecture with a modified contracting path. We use the CNN to generate an initial segmentation of the lesion, then refine it by running the watershed algorithm on high-confidence pixels. We train the network on 247 images with a variety of lesion sizes, complexity, and anatomical sites. The network with our modifications noticeably outperforms the state-of-the-art U-Net, with a Jaccard Index (JI) score of 73.6% (compared to 36.7%). Moreover, our method requires only a few seconds for segmentation, in contrast with the previously proposed semi-autonomous watershed approach, which requires 2-29 minutes per image.