Since abnormal expression of long non-coding RNAs (lncRNAs) is associated with various human diseases, identifying disease-related lncRNAs helps reveal the pathogenesis of diseases. Existing methods for lncRNA-disease association prediction mainly focus on multi-sourced data related to lncRNAs and diseases. The rich semantic information of meta-paths, composed of multiple kinds of connections between lncRNA and disease nodes, is neglected. We propose a new prediction method, MGLDA, to encode and integrate the semantics of multiple meta-paths, the global topology of heterogeneous graph, and pairwise attributes of lncRNA and disease nodes. First, a tri-layer heterogeneous graph is constructed to associate multi-sourced data across the lncRNA, disease, and miRNA nodes. Afterwards, we establish multiple meta-paths connecting the lncRNA and disease nodes to derive and denote various semantics. Each meta-path contains its specific semantics formulated by an embedding strategy, and each embedding covers local topology formed by the diverse semantic connections among the lncRNA, disease, and miRNA nodes. We construct multiple graph convolutional autoencoders (GCA) with topology-level attention to learn global and multiple local topologies from the tri-layer graph and each meta-path, respectively. The topology-level attention mechanism can learn the importance of various global and local topologies for adaptive pairwise topology fusion. Finally, a convolutional autoencoder learns the attribute representations of lncRNA-disease pairs, which integrates the learnt detailed and representative pairwise features. Experimental results show that MGLDA outperforms other state-of-the-art prediction methods in comparison and retrieves more real lncRNA-disease associations in the top-ranked candidates. The ablation study also demonstrates the important contributions of the local and global topology learning, and pairwise attribute learning. Case studies on three diseases further demonstrate MGLDA's ability to identify potential disease-related lncRNAs.