Accurate decoding of lower-limb motion from EEG signals is essential for advancing brain-computer interface (BCI) applications in movement intent recognition and control. This study presents NeuroDyGait, a two-stage, phase-aware EEG-to-gait decoding framework that explicitly models temporal continuity and domain relationships. To address challenges of causal, phase-consistent prediction and cross-subject variability, Stage I learns semantically aligned EEG-motion embeddings via relative contrastive learning with a cross-attention-based metric, while Stage II performs domain relation-aware decoding through dynamic fusion of session-specific heads. Comprehensive experiments on two benchmark datasets (GED and FMD) show substantial gains over baselines, including a recent 2025 model EEG2GAIT. The framework generalizes to unseen subjects and maintains inference latency below 5 ms per window, satisfying real-time BCI requirements. Visualization of learned attention and phase-specific cortical saliency maps further reveals interpretable neural correlates of gait phases. Future extensions will target rehabilitation populations and multimodal integration.