Abnormal expressions of long non-coding RNAs (lncRNAs) are associated with various human diseases. Identifying disease-related lncRNAs can help clarify complex disease pathogeneses. The latest methods for lncRNA-disease association prediction rely on diverse data about lncRNAs and diseases. These methods, however, cannot adequately integrate the neighbour topological information of lncRNA and disease nodes. Moreover, more intrinsic features of lncRNA-disease node pairs can be explored to better predict their latent associations. We developed a novel method, named GTAN, to predict the association propensities between lncRNAs and diseases. GTAN integrates various information about lncRNAs and diseases, and exploits neighbour topology and attribute representations of a pair of lncRNA-disease nodes. We adopted in GTAN a graph neural network architecture with three attention mechanisms and multi-layer convolutional neural networks. First, a neighbour-level self-attention mechanism is constructed to learn the importance of each neighbour for an interested lncRNA or disease node. Second, topology-level attention is proposed to enhance contextual dependencies among multiple local topology representations. An attention-enhanced graph neural network framework is then established to learn a topology representation of top-ranked neighbours. GTAN also has attribute-level attention to distinguish various contributions of attributes of the lncRNA-disease pair. Finally, attribute representation is learned by multi-layer CNN to integrate detailed features and representative features of the pair. Extensive experimental results demonstrated that GTAN outperformed state-of-the-art methods. The ablation studies confirmed the important contributions of three attention mechanisms. Case studies on three cancers further showed GTAN's ability in discovering potential lncRNA candidates related to diseases.