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Heteroanionic hydrides offer great possibilities in the design of functional materials. For ternary rare earth hydride oxide <i>RE</i>HO, several modifications were reported with indications for a significant phase width with respect to H and O of the cubic representatives. We obtained DyHO and ErHO as well as the thus far elusive LuHO from solid-state reactions of <i>RE</i>₂O₃ and <i>RE</i>H₃ or LuH₃ with CaO and investigated their crystal structures by neutron and X-ray powder diffraction. While DyHO, ErHO, and LuHO adopted the cubic anion-ordered half-Heusler LiAlSi structure type (<i>F</i><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover><mn>4</mn><mo>¯</mo></mover></mrow></semantics></math></inline-formula>3<i>m</i>, <i>a</i>(DyHO) = 5.30945(10) Å, <i>a</i>(ErHO) = 5.24615(7) Å, <i>a</i>(LuHO) = 5.171591(13) Å), LuHO additionally formed the orthorhombic anti-LiMgN structure type (<i>Pnma</i>; LuHO: <i>a</i> = 7.3493(7) Å, <i>b</i> = 3.6747(4) Å, <i>c</i> = 5.1985(3) Å; LuDO: <i>a</i> = 7.3116(16) Å, <i>b</i> = 3.6492(8) Å, <i>c</i> = 5.2021(7) Å). A comparison of the cubic compounds’ lattice parameters enabled a significant distinction between <i>RE</i>HO and <i>RE</i>H_1+2<i>x</i>O_1−<i>x</i> (<i>x</i> < 0 or <i>x</i> > 0). Furthermore, a computational chemistry study revealed the formation of <i>RE</i>HO compounds of the smallest rare earth elements to be disfavored in comparison to the sesquioxides, which is why they may only be obtained by mild synthesis conditions.