  We consider three fermions with two spin components interacting on a lattice
model with an infinite scattering length. Low lying eigenenergies in a cubic
box with periodic boundary conditions, and for a zero total momentum, are
calculated numerically for decreasing values of the lattice period. The results
are compared to the predictions of the zero range Bethe-Peierls model in
continuous space, where the interaction is replaced by contact conditions. The
numerical computation, combined with analytical arguments, shows the absence of
negative energy solution, and a rapid convergence of the lattice model towards
the Bethe-Peierls model for a vanishing lattice period. This establishes for
this system the universality of the zero interaction range limit.
