Motivated by the recent report of room-temperature superconductivity at near-ambient pressure in N-doped lutetium hydride, we performed a comprehensive, detailed study of the phase diagram of the Lu–N–H system, looking for superconducting phases. We combined ab initio crystal structure prediction with ephemeral data- derived interatomic potentials to sample over 200,000 different structures. Out of the more than 150 structures predicted to be metastable within ∼ 50 meV from the convex hull we identify 52 viable candidates for con- ventional superconductivity, for which we computed their superconducting properties from Density Functional Perturbation Theory. Although for some of these structures we do predict a finite superconducting Tc, none is even remotely compatible with room-temperature superconductivity as reported by Dasenbrock et al. Our work joins the broader community effort that has followed the report of near-ambient superconductivity, confirming beyond reasonable doubt that no conventional mechanism can explain the reported Tc in Lu–N–H.