Towards automated retinal screening, this paper makes an endeavor to simultaneously achieve pixel-level retinal lesion segmentation and image-level disease classification. Such a multi-task approach is crucial for accurate and clinically interpretable disease diagnosis. Prior art is insufficient due to three challenges, that is, lesions lacking objective boundaries, clinical importance of lesions irrelevant to their size, and the lack of one-to-one correspondence between lesion and disease classes. This paper attacks the three challenges in the context of diabetic retinopathy (DR) grading. We propose L-Net, a new variant of fully convolutional networks, with its expansive path re-designed to tackle the first challenge. A dual loss that leverages both semantic segmentation and image classification losses is devised to resolve the second challenge. We propose Side-Attention Net (SiAN) as our multi-task framework. Harnessing L-Net as a side-attention branch, SiAN simultaneously improves DR grading and interprets the decision with lesion maps. A set of 12K fundus images is manually segmented by 45 ophthalmologists for 8 DR-related lesions, resulting in 290K manual segments in total. Extensive experiments on this large-scale dataset show that our proposed approach surpasses the prior art for multiple tasks including lesion segmentation, lesion classification and DR grading.