Using a comprehensive structure search and high-throughput first-principles calculations of 1483 compounds, this study presents the phase diagram Lu-H-N. The formation energy landscape Lu-H-N was derived utilized to assess thermodynamic stability compounds. Results indicate that there are no stable ternary structures in system, but metastable structures, such as Lu20H2N17 (C2/m), Lu2H2N (P3-m1)...