  The type-II Dirac cone is a special feature of the band structure, whose
Fermi level is represented by a pair of crossing lines. It has been
demonstrated that such a structure is useful for investigating topological edge
solitons, and more specifically, for mimicking the Kline tunneling. However, it
is still not clear what the interplay between type-II Dirac cones and the
non-Hermiticity mechanism will result in. Here, this question is addressed; in
particular, we report the $\mathcal{PT}$-symmetric photonic lattices with
type-II Dirac cones for the first time. We identify a slope-exceptional ring
and name it the type-II exceptional ring. We display the restoration of the
$\mathcal{PT}$ symmetry of the lattice by reducing the separation between the
sites in the unit cell. Curiously, the amplitude of the beam during propagation
in the non-Hermitian lattice with $\mathcal{PT}$ symmetry only decays because
of diffraction, whereas in the $\mathcal{PT}$ symmetry-broken lattice it will
be amplified, even though the beam still diffracts. This work establishes the
link between the non-Hermiticity mechanism and the violation of Lorentz
invariance in these physical systems.
