Although deep learning for Diabetic Retinopathy (DR) screening has shown great success in achieving clinically acceptable accuracy for referable versus non-referable DR, there remains a need to provide more fine-grained grading of the DR severity level as well as automated segmentation of lesions (if any) in the retina images. We observe that the DR severity level of an image is dependent on the presence of different types of lesions and their prevalence. In this work, we adopt a multi-task learning approach to perform the DR grading and lesion segmentation tasks. In light of the lack of lesion segmentation mask ground-truths, we further propose a semi-supervised learning process to obtain the segmentation masks for the various datasets. Experiments results on publicly available datasets and a real world dataset obtained from population screening demonstrate the effectiveness of the multi-task solution over state-of-the-art networks.