  We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model with
both $g_x^2(\bar{\psi}\psi)^2$ and $g_y^2(\bar{\psi}i\gamma_5\psi)^2$
interaction terms on a spatial lattice. The continuous chiral symmetry, which
is present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooft
anomaly with the charge conservation symmetry, which guarantees the existence
of a massless mode. However, the same 't~Hooft anomaly also implies that the
continuous chiral symmetry is broken explicitly in our lattice model.
Nevertheless, from numerical matrix product state simulations we find that, for
certain parameters of the lattice model, the continuous chiral symmetry
reemerges in the infrared fixed point theory, even at strong coupling. We argue
that, to understand this phenomenon, it is crucial to go beyond mean-field
theory (or, equivalently, beyond the leading order term in a $1/N$ expansion).
Interestingly, on the lattice, the chiral Gross-Neveu model appears at a
Landau-forbidden second order phase transition separating two distinct and
unrelated symmetry-breaking orders. We point out the crucial role of two
different 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for this
Landau-forbidden phase transition to occur.
