  We report quantum Monte Carlo calculations of single-$\Lambda$ hypernuclei
for $A<50$ based on phenomenological two- and three-body hyperon-nucleon
forces. We present results for the $\Lambda$ separation energy in different
hyperon orbits, showing that the accuracy of theoretical predictions exceeds
that of currently available experimental data, especially for medium-mass
hypernuclei. We show the results of a sensitivity study that indicates the
possibility to investigate the nucleon-isospin dependence of the three-body
hyperon-nucleon-nucleon force in the medium-mass region of the hypernuclear
chart, where new spectroscopy studies are currently planned. The importance of
such a dependence for the description of the physics of hypernuclei, and the
consequences for the prediction of neutron star properties are discussed.
