Clinical treatment of skin lesion is primarily dependent on timely detection and delimitation of lesion boundaries for accurate cancerous region localization. Prevalence of skin cancer is on the higher side, especially that of melanoma, which is aggressive in nature due to its high metastasis rate. Therefore, timely diagnosis is critical for its treatment before the onset of malignancy. To address this problem, medical imaging is used for the analysis and segmentation of lesion boundaries from dermoscopic images. Various methods have been used, ranging from visual inspection to the textural analysis of the images. However, accuracy of these methods is low for proper clinical treatment because of the sensitivity involved in surgical procedures or drug application. This presents an opportunity to develop an automated model with good accuracy so that it may be used in a clinical setting. This paper proposes an automated method for segmenting lesion boundaries that combines two architectures, the U-Net and the ResNet, collectively called Res-Unet. Moreover, we also used image inpainting for hair removal, which improved the segmentation results significantly. We trained our model on the ISIC 2017 dataset and validated it on the ISIC 2017 test set as well as the PH2 dataset. Our proposed model attained a Jaccard Index of 0.772 on the ISIC 2017 test set and 0.854 on the PH2 dataset, which are comparable results to the current available state-of-the-art techniques.