It is well known that the unusual expression of long non-coding RNAs (lncRNAs) is closely related to the physiological and pathological processes of diseases. Therefore, inferring the potential lncRNA–disease associations are helpful for understanding the molecular pathogenesis of diseases. Most previous methods have concentrated on the construction of shallow learning models in order to predict lncRNA-disease associations, while they have failed to deeply integrate heterogeneous multi-source data and to learn the low-dimensional feature representations from these data. We propose a method based on the convolutional neural network with the attention mechanism and convolutional autoencoder for predicting candidate disease-related lncRNAs, and refer to it as CNNDLP. CNNDLP integrates multiple kinds of data from heterogeneous sources, including the associations, interactions, and similarities related to the lncRNAs, diseases, and miRNAs. Two different embedding layers are established by combining the diverse biological premises about the cases that the lncRNAs are likely to associate with the diseases. We construct a novel prediction model based on the convolutional neural network with attention mechanism and convolutional autoencoder to learn the attention and the low-dimensional network representations of the lncRNA–disease pairs from the embedding layers. The different adjacent edges among the lncRNA, miRNA, and disease nodes have different contributions for association prediction. Hence, an attention mechanism at the adjacent edge level is established, and the left side of the model learns the attention representation of a pair of lncRNA and disease. A new type of lncRNA similarity and a new type of disease similarity are calculated by incorporating the topological structures of multiple bipartite networks. The low-dimensional network representation of the lncRNA-disease pairs is further learned by the autoencoder based convolutional neutral network on the right side of the model. The cross-validation experimental results confirm that CNNDLP has superior prediction performance compared to the state-of-the-art methods. Case studies on stomach cancer, breast cancer, and prostate cancer further show the ability of CNNDLP for discovering the potential disease lncRNAs.