  A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is
developed, based on the continuum theory presented in the preceding paper.
Special attention is given to choosing a lattice action (the ``geodesic''
action) that is appropriate for fields having noncompact curved configuration
spaces. A consistent continuum limit of the model exists only if the
renormalized scale constant $\beta_R$ vanishes for some value of the bare scale
constant~$\beta$. The geodesic action has a special form that allows direct
access to the small-$\beta$ limit. In this limit half of the degrees of freedom
can be integrated out exactly. The remaining degrees of freedom are those of a
compact model having a $\beta$-independent action which is noteworthy in being
unbounded from below yet yielding integrable averages. Both the exact action
and the $\beta$-independent action are used to obtain $\beta_R$ from Monte
Carlo computations of field-field averages (2-point functions) and
current-current averages. Many consistency cross-checks are performed. It is
found that there is no value of $\beta$ for which $\beta_R$ vanishes. This
means that as the lattice cutoff is removed the theory becomes that of a pair
of massless free fields. Because these fields have neither the geometry nor the
symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$
model has no continuum limit.
