The search for materials with intrinsically low thermal conductivity (κ_L) is critical for energy applications, yet conventional descriptors often fail to capture the complex interplay between bonding and lattice dynamics. Here, first-principles calculations are used to contrast the thermal transport in covalent zincblende (zb) and metavalent rocksalt (rs) BeO. We find that the metavalent bonding in rs-BeO enhances lattice anharmonicity, activating multi-phonon scattering channels and suppressing phonon transport. This results in an ultralow κ_L of 24 W m⁻¹ K⁻¹ at 300 K, starkly contrasting with the zb phase (357 W m⁻¹ K⁻¹). Accurately modeling such strongly anharmonic systems requires explicit inclusion of temperature-dependent phonon renormalization and four-phonon scattering. These contributions, negligible in zb-BeO, are essential for high-precision calculations of the severely suppressed κ_L in rs-BeO. Finally, we identify three key indicators to guide the discovery of metavalently bonded, incipient-metallic materials: (i) an NaCl-type crystal structure, (ii) large Grüneisen parameters (textgreater2), and (iii) a breakdown of the Lyddane-Sachs-Teller relation. These findings provide microscopic insight into thermal transport suppression by metavalent bonding and offer a predictive framework for identifying promising thermoelectrics and phase-change materials.