Diabetic retinopathy (DR) is a severe eye disease which can lead to permanent blindness. Identifying DR in early stages by using computer-aided diagnosis (CAD) systems can help the ophthalmologists to give proper treatment rationally, there by preventing many people from going blind. Due to intra-class variations and imbalanced data distribution, it is highly difficult to design a CAD system for DR severity diagnosis with greater generalizability. In this article, we propose a multi-stage deep learning pipeline, lesion-aware attention with neural support vector machine, for diabetic retinopathy diagnosis. Proposed pipeline consists of a pre-trained convolution base for learning retinal image spatial representations, lesion-aware attention for weighting lesion specific features, convolution autoencoder for learning latent attention representations and a neural support vector machine for discrimination. Convolutional autoencoder and neural support vector machine are jointly trained in end-to-end fashion to obtain category based lesion specific latent attention features by complementing each other in re-constructor and discriminator paths. Proposed approach is validated using two benchmark retinal scan image datasets, Kaggle APTOS 2019 and ISBI 2018 IDRiD, for DR type and severity grade classification tasks. Our experimental studies expose that using lesion-aware attention along with the joint training of autoencoder and neural support vector machine boosted the performance of models used for DR diagnosis, thereby outperforming existing works presented in the literature for DR severity grading. Proposed model achieved the highest accuracy of 90.45%, 84.31% on APTOS dataset and an accuracy of 79.85%, 63.24% on IDRiD dataset for DR type and severity grade classification tasks, respectively.