  We give Gr\"obner-Shirshov bases for Drinfeld-Kohno Lie algebra
$\textbf{L}_{n}$ in \cite{[Et]} and Kukin Lie algebra $A_P$ in \cite{Kukin},
where $P$ is a semigroup. As applications, we show that as $\mathbb{Z}$-module
$\textbf{L}_{n}$ is free and a $\mathbb{Z}$-basis of $\textbf{L}_{n}$ is given.
We give another proof of Kukin Theorem: if semigroup $P$ has the undecidable
word problem then the Lie algebra $A_P$ has the same property.
