  In \cite{G-Z} G.~Ghosh and W. Zwonek introduced a new class of domains
$\bL_n$, $n\ge1$, which are 2-proper holomorphic images of the Cartan domains
of type four. This family contains biholomorphic images of the symmetrized
bidisc and the tetrablock. It is well-known, that symmetrized bidisc and
tetrablock are Lempert type domains. In our paper we show that the whole family
of domains $\bL_n$ are Lempert domains.
