Cardiovascular disease has become the leading cause of death worldwide, underscoring the urgent need for widespread cardiac monitoring, while the Electrocardiogram (ECG) remains the diagnostic gold standard, the complexity of its acquisition limits its long-term feasibility. In contrast, Photoplethysmography (PPG), ubiquitous in wearable devices, is increasingly adopted due to its accessibility. However, synthesizing ECG from PPG poses an intrinsically ill-posed inverse problem. Existing purely data-driven paradigms often neglect underlying biophysical mechanisms, resulting in a lack of physical constraints and interpretability, which renders them prone to generating non-physiological hallucinations. To address this, we propose PhysDiff-LBM, a novel physics-aware framework that incorporates Lattice Boltzmann hemodynamic constraints into a conditional diffusion model. Employing a dual-stream architecture, our framework captures high-frequency morphological details via a cross-attention-guided diffusion model with region-wise adaptability. Synergistically, we physically regularize the ECG synthesis by leveraging the mesoscopic streaming and collision operators of LBM. By forcing the synthesized waveform gradients to evolve consistently with hemodynamic momentum, this mechanism constrains the model to strictly adhere to the fluid dynamic conservation laws governing pulse wave propagation. Experimental results demonstrate that our method achieves superior signal fidelity and exhibits significant advantages in downstream clinical applications.