Sequence-based protein-protein interaction (PPI) prediction represents a fundamental computational biology problem. To address this problem, extensive research efforts have been made to extract predefined features from the sequences. Based on these features, statistical algorithms are learned to classify the PPIs. However, such explicit features are usually costly to extract, and typically have limited coverage on the PPI information. Hence, we present an end-to-end framework, Lasagna, for PPI predictions using only the primary sequences of a protein pair. Lasagna incorporates a deep residual recurrent convolutional neural network in the Siamese learning architecture, which leverages both robust local features and contextualized information that are significant for capturing the mutual influence of protein sequences. Our framework relieves the data pre-processing efforts that are required by other systems, and generalizes well to different application scenarios. Experimental evaluations show that Lasagna outperforms various state-of-the-art systems on the binary PPI prediction problem. Moreover, it shows a promising performance on more challenging problems of interaction type prediction and binding affinity estimation, where existing approaches fall short. The implementation of our framework is available at https://github.com/muhaochen/seq_ppi.git