This paper gives rudiments of Lie algebras over commutative von Neumann algebras up to the fundamental structure and representation theorems. Although finite-dimensionality in Boolean valued sense is assumed, it is much weaker than finite-dimensionality in the usual sense, and the theory can be regarded as a mild infinite-dimensional generalization of the well-established theory of finite-dimensional Lie algebras over complex numbers. The principal technique we use is a transfer principle from standard mathematics to Boolean-valued mathematics, for such infinite- dimensional Lie algebras can be regarded as Boolean-valued finite- dimensional Lie algebras over complex numbers.