  We demonstrate mesoscopic transport through quantum states in quasi-1D
lattices maintaining the combination of parity and time-reversal symmetries by
controlling energy gain and loss. We investigate the phase diagram of the
non-Hermitian system where transitions take place between unbroken and broken
$\mathcal{PT}$-symmetric phases via exceptional points. Quantum transport in
the lattice is measured only in the unbroken phases in the energy band-but not
in the broken phases. The broken phase allows for spontaneous symmetry-broken
states where the cross-stitch lattice is separated into two identical single
lattices corresponding to conditionally degenerate eigenstates. These
degeneracies show a lift-up in the complex energy plane, caused by the
non-Hermiticity with $\mathcal{PT}$-symmetry.
