  We present a theoretical study on the robustness of multi-photon states in a
frustrated lattice of coupled nonlinear optical cavities, which are described
by a driven-dissipative Bose-Hubbard model. In particular, we focus here on a
Lieb lattice with two elementary cells and periodic boundary conditions. Due to
the geometric frustration of the lattice, the non-equilibrium steady state can
exhibit dark sites with low photon density and strong correlations, ascribable
to the population of multi-photon modes. We explore the sensitivity of such
strong correlations on the random inhomogeneity of the lattice parameters. We
show that the correlations are more sensitive to the inhomogeneity of the
cavity frequencies than to the random fluctuations of the hopping strength.
