  The massive two-dimensional Nambu--Jona-Lasinio model with isospin (isoNJL)
is reconsidered in the large $N_c$ limit. We continue the exploration of its
phase diagram by constructing missing first-order phase boundaries. At zero
temperature, a phase boundary in the plane of baryon and isospin chemical
potentials separates the vacuum from a crystal phase. We derive it from the
baryon spectrum of the isoNJL model which, in turn, is obtained via a numerical
Hartree-Fock (HF) calculation. At finite temperature, a first-order phase
boundary sheet is found using a thermal HF calculation. It interpolates
smoothly between the zero temperature phase boundary and the perturbative
sheet. The calculations remain tractable owing to the assumption that the
charged pion condensate vanishes. In that case, most of the calculations can be
done with methods developed in the past for solving the massive one-flavor NJL
model.
