We study a three-orbital Su-Schrieffer-Heeger model defined on a two-dimensional Lieb lattice and in the negative charge transfer regime using determinant quantum Monte Carlo. At half-filling (1 hole/unit cell), we observe a bipolaron insulating phase, where the ligand oxygen atoms collapse and expand about alternating cation atoms to produce a bond-disproportionated state. This phase is robust against moderate hole doping but is eventually suppressed at large hole concentrations, leading to a metallic polaron-liquid-like state with fluctuating patches of local distortions. Our results suggest that the polarons are highly disordered in the metallic state and freeze into a periodic array across the metal-to-insulator transition. We also find an $s$-wave superconducting state at finite doping that primarily appears on the oxygen sublattices. Our approach provides an efficient, non-perturbative way to treat bond phonons in higher dimensions and our results have implications for many materials where coupling to bond phonons is the dominant interaction.
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