Friend link prediction is an important issue in recommendation systems and social network analysis. In Location-Based Social Networks (LBSNs), predicting potential friend relationships faces significant challenges due to the diversity of user behaviors, along with the high dimensionality, sparsity, and complex noise in the data. To address these issues, this paper proposes a Heterogeneous Graph Attention Network (GEVEHGAN) model based on Lite Gate Recurrent Unit (Lite-GRU) embedding and Variational Autoencoder (VAE) enhancement. The model constructs a heterogeneous graph with two types of nodes and three types of edges; combines Skip-Gram and Lite-GRU to learn Point of Interest (POI) and user node embeddings; introduces VAE for dimensionality reduction and denoising of the embeddings; and employs edge-level attention mechanisms to enhance information propagation and feature aggregation. Experiments are conducted on the publicly available Foursquare dataset. The results show that the GEVEHGAN model outperforms other comparative models in evaluation metrics such as AUC, AP, and Top@K accuracy, demonstrating its superior performance in the friend link prediction task.