Legal judgment prediction (LJP) increasingly relies on large language models whose full fine-tuning is memory-intensive and susceptible to catastrophic forgetting. We present LawLLM-DS, a two-stage Low-Rank Adaptation (LoRA) framework that first performs legal knowledge pre-tuning with an aggressive learning rate and subsequently refines judgment relations with conservative updates, using dedicated LoRA adapters, 4-bit quantization, and targeted modification of seven Transformer projection matrices to keep only 0.21% of parameters trainable. From a structural perspective, the twenty annotated legal elements form a symmetric label co-occurrence graph that exhibits both cluster-level regularities and asymmetric sparsity patterns, and LawLLM-DS implicitly captures these graph-informed dependencies while remaining compatible with downstream GNN-based representations. Experiments on 5,096 manually annotated divorce cases show that LawLLM-DS lifts macro F1 to 0.8893 and achieves an accuracy of 0.8786, outperforming single-stage LoRA and BERT baselines under the same data regime. Ablation studies further verify the contributions of stage-wise learning rates, adapter placement, and low-rank settings. These findings demonstrate that curriculum-style, parameter-efficient adaptation provides a practical path toward lightweight yet structure-aware LJP systems for judicial decision support.