  In this article, we discuss Lie nilpotency and Lie solvability of non-abelian
tensor product of multiplicative Lie algebras. In particular, for giving
information concerning the Lie nilpotency (or Lie solvability) of either
multiplicative Lie algebras $G$ or $H,$ the non-abelian tensor product $
\frac{G\otimes H}{I}$ is Lie nilpotent (or Lie solvable), for some ideal $I$ of
${G\otimes H}$.
