The effectiveness of mathematics in describing nature has long invited philosophical explanation. This paper examines whether Lie algebra embodies organizational principles that extend beyond its traditional role in symmetry analysis. Beginning with the fundamental properties of Lie brackets, including antisymmetry, bilinearity, the Jacobi identity, and the derived relation [��,−��]=0, it is argued that Lie algebra provides a formal grammar of relational coherence. Particular attention is given to the invariance of Lie-algebraic structure under global reflection ��↦−��, which preserves brackets and relational organization while remaining indifferent to overall orientation. This observation motivates the claim that relational structure alone may not uniquely determine ontological orientation. Connections are explored with CPT symmetry, electromagnetism, active inference, developmental biology, and multiscale regulation, while carefully distinguishing mathematical results from heuristic interpretation. The paper does not claim that Lie algebra proves ontological two-sidedness or derives physical symmetries. Rather, it argues that Lie-theoretic structures exhibit a remarkable compatibility with coherent organization across multiple domains and therefore leave two-sided ontological interpretations admissible. In this view, the effectiveness of mathematics may arise because both mathematics and nature instantiate common principles of relational coherence and regulated organization.