Legal case retrieval (LCR) is a specialised information retrieval task aimed at identifying relevant cases given a query case. LCR holds pivotal significance in facilitating legal practitioners to locate legal precedents. Existing LCR methods predominantly rely on traditional lexical models or language models; however, they typically overlook the domain-specific structural information embedded in legal documents. Our previous work CaseGNN successfully harnesses text-attributed graphs and graph neural networks to incorporate structural legal information. Nonetheless, three key challenges remain in enhancing the representational capacity of CaseGNN: (1) The under-utilisation of rich edge information in text-attributed case graph (TACG). (2) The insufficiency of training signals for graph contrastive learning. (3) The lack of contextualised legal information in node and edge features. In this paper, the LEXA model, an extension of CaseGNN, is proposed to overcome these limitations by jointly leveraging rich edge information, enhanced training signals, and contextualised embeddings derived from large language models (LLMs). Specifically, an edge-updated graph attention layer (EUGAT) is proposed to comprehensively update node and edge features during graph modelling, resulting in a full utilisation of structural information of legal cases. Moreover, LEXA incorporates a novel graph contrastive learning objective with graph augmentation to provide additional training signals, thereby strengthening the model's legal comprehension capabilities. What's more, LLMs are employed to generate node and edge features for TACG. Extensive experiments on two benchmark datasets demonstrate that LEXA not only significantly improves CaseGNN but also achieves supreme performance compared to state-of-the-art LCR methods.