Irr. representations of semi-direct product of Lie algebras

Question

Let $g_{1}$, $g_{2}$ be Lie algebras , $g_{1} \oplus g_{2}$ their direct sum. As a vector space it is a direct sum of $g_{1}$ and $g_{2}$ and Lie algebra structure is given by $[(x,y),(x',y')]=([x,x'],[y,y'])$. Is it true that every irreducible representation of $g_{1}\oplus g_{2}$ is isomorphic to $V_{1}\otimes V_{2}$ where $V_{1}$, $V_{2}$ are irreducible represenrations of $g_{1}$, $g_{2}$ respectively?