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We present a theoretical study on the robustness of multi-photon states in afrustrated lattice of coupled nonlinear optical cavities, which are describedby a driven-dissipative Bose-Hubbard model. In particular, we focus here on aLieb lattice with two elementary cells and periodic boundary conditions. Due tothe geometric frustration of the lattice, the non-equilibrium steady state canexhibit dark sites with low photon density and strong correlations, ascribableto the population of multi-photon modes. We explore the sensitivity of suchstrong correlations on the random inhomogeneity of the lattice parameters. Weshow that the correlations are more sensitive to the inhomogeneity of thecavity frequencies than to the random fluctuations of the hopping strength.

On the robustness of strongly correlated multi-photon states in frustrated driven-dissipative cavity lattices