  We extend a chiral effective field theory approach to the $\Lambda$-nuclei
interaction with the inclusion of the decuplet baryons. More precisely, we
study the contributions due to the long-range two-pion exchange, with $\Sigma$
and $\Sigma^*$ baryons in the internal baryonic lines considering Nh and
$\Delta$h excitations. In particular, central and spin-orbit potentials are
studied. For the former, regularization is needed and physical values of the
cut-off give a large attraction, becoming necessary to include the repulsion of
other terms not considered here. For the latter, in a model-independent
framework, the inclusion of the decuplet supports the natural explanation of
the smallness of the $\Lambda$-nuclear spin-orbit term and shows the importance
of the $\Sigma^*$ and $\Delta$ degrees of freedom for the hyperon-nucleus
interactions.
