We have experimentally studied the temperature range and conditions of the stable operation of rare-earth metal (REM) vapor lasers. Gas-discharge tubes made of alumina (Al₂O₃-GDTs) were used in the experiments. The lasing appears at the temperature when the saturated-vapor pressure of REMs reaches the value of 0.1 Torr and abruptly drops at the melting temperature of corresponding REM under any excitation conditions. The necessity of protecting film of REM aluminates Ln_nAl_mO_k and oxides Ln₂O₃ on the inner surface of Al₂O₃-GDT for stable operation of these lasers is shown. An explanation of lasing impossibility in vapors of cerium (Ce), praseodymium (Pr), neodymium (Nd), gadolinium (Gd), and terbium (Tb) under gas-discharge excitation is proposed.