  Open, non-equilibrium systems with balanced gain and loss, known as
parity-time ($\mathcal{PT}$)-symmetric systems, exhibit properties that are
absent in closed, isolated systems. A key property is the
$\mathcal{PT}$-symmetry breaking transition, which occurs when the gain-loss
strength, a measure of the openness of the system, exceeds the intrinsic
energy-scale of the system. We analyze the fate of this transition in
disordered lattices with non-Hermitian gain and loss potentials $\pm i\gamma$
at reflection-symmetric sites. Contrary to the popular belief, we show that the
$\mathcal{PT}$-symmetric phase is protected in the presence of a correlated
(periodic) disorder which leads to a positive $\mathcal{PT}$-symmetry breaking
threshold. We uncover a veiled symmetry of such disordered systems that is
instrumental for the said protection, and show that this symmetry leads to new
localization behavior across the $\mathcal{PT}$-symmetry breaking transition.
We elucidate the interplay between such localization and the
$\mathcal{PT}$-symmetry breaking phenomena in disordered
$\mathcal{PT}$-symmetric lattices, and support our conclusions with a
beam-propagation-method analysis. Our theoretical predictions provide avenues
for experimental realizations of $\mathcal{PT}$-symmetric systems with
engineered disorder.
