  We analyze the vacuum structure of a generalized lattice Nambu--Jona-Lasinio
model with two flavors of Wilson fermions, such that its continuum action is
the most general four-fermion action with 'trivial' color interactions, and
having a $SU(2)_V x SU(2)_A$ symmetry in the chiral limit. The phase structure
of this model in the space of the two four-fermion couplings shows, in addition
to the standard Aoki phases, new phases with $<\bar\psi \gamma_5\psi> != 0$, in
close analogy to similar results recently suggested by some of us for lattice
QCD with two degenerate Wilson fermions. This result shows how the phase
structure of an effective model for low energy QCD cannot be entirely
understood from Wilson Chiral Perturbation Theory, based on the standard QCD
chiral effective Lagrangian approach.
