<p>This dataset presents the results of a comprehensive crystal structure search for ternary compounds in the Lu–N–H system. Thousands of candidate structures were evaluated, and their thermodynamic stability was assessed through the construction of the convex hull of formation enthalpies. To ensure reliable energetic ordering, all calculations were performed using the highly accurate r2SCAN density functional in an all-electron framework, avoiding possible pseudopotential-related inaccuracies.  A previously unreported lutetium hydride phase (HLu₂) is identified on the convex hull, indicating thermodynamic stability. However, subsequent electron–phonon coupling analysis shows that this structure is not a promising candidate for near-ambient superconductivity. Apart from this additional phase, the results are in close agreement with earlier structure prediction studies, demonstrating strong reproducibility across independent computational approaches. This consistency highlights the maturity and reliability of modern crystal structure prediction methods. Overall, the dataset provides further evidence that no thermodynamically stable structure within the Lu–N–H system is likely to exhibit conventional high-temperature superconductivity under near-ambient conditions, as would be required to explain previously reported experimental claims.</p>