  We show that the so called $\lambda$ deformed $\sigma$-model as well as the
$\eta$ deformed one belong to a class of the ${\cal E}$-models introduced in
the context of the Poisson-Lie-T-duality. The $\lambda$ and $\eta$ theories
differ solely by the choice of the Drinfeld double; for the $\lambda$ model the
double is the direct product $G\times G$ while for the $\eta$ model it is the
complexified group $G^{\mathbb{C}}$. As a consequence of this picture, we prove
for any $G$ that the target space geometries of the $\lambda$-model and of the
Poisson-Lie T-dual of the $\eta$-model are related by a simple analytic
continuation.
