  In the last years auxiliary field diffusion Monte Carlo has been used to
assess the properties of hypernuclear systems, from light- to medium-heavy
hypernuclei and hyper-neutron matter. One of the main findings is the key role
played by the three-body hyperon-nucleon-nucleon interaction in the
determination of the hyperon separation energy of hypernuclei and as a possible
solution to the hyperon puzzle. However, there are still aspects of the
employed hypernuclear potential that remain to be carefully investigated. In
this paper we show that the isospin dependence of the Lambda-NN force, which is
crucial in determining the NS structure, is poorly constrained by the available
experimental data.
