  We obtain off-critical (elliptic) Boltzmann weights for lattice models whose
continuum limits correspond to massive, $N=2$ supersymmetric, quantum
integrable field theories. We also compute the free energies of these models
and show that they are analytic in the region of parameter space where we
believe that the supersymmetry is unbroken. While the supersymmetry is not
directly realized on the lattice, there is still a very close connection
between the models described here and topological lattice models. A simple
example is discussed in detail and some corner transfer matrix computations are
also presented.
