The research on the superconductivity of hydrogen-rich compounds has become a hot research topic in the field of high-temperature superconductors in recent years and yttrium hydride YH_9+x has been experimentally confirmed to have high temperature superconductivity (near room temperature (Tc = 262 K)), following behind the research of H₃S (Tc = 200 K) and LaH₁₀ (Tc = 260 K). The theoretical study of binary hydrogen-rich systems is relatively mature, while the structural characteristics and superconductivity of ternary or quaternary hydrogen-rich compounds are still under exploration. In this paper, nLiH + YH₃→Li_nYH_n+3 (<i>n</i> = 1–3) is the synthesis way to explore the stable configuration of ternary hydride LinYH_n+3 in a pressure range of 0–300 GPa. The crystal structure, electronic structure, thermodynamic and kinetic stability of LiYH₄, Li₂YH₅ and Li₃YH₆ in the pressure range of 0–300 GPa are studied based on the structure prediction by particle swarm optimization algorithm and first-principles calculation. The CALYPSO method is used to search for 1–4 times molecular formula structures for Li-Y-H ternary systems with different stoichiometric ratios in the pressure range of 0–300 GPa in steps of 50 GPa. The results show that LiYH₄-<i>P</i>4/<i>nmm</i>, Li₂YH₅-<i>I</i>4/<i>mmm</i>, and Li₃YH₆-P4/nmm can be respectively synthesized with a certain ratio between LiH and YH₃ respectively in a pressure range of 169–221 GPa, 141–300 GPa and 166–300 GPa. The Li₂YH₅ has the lowest stable pressure and widest range which can be the possible choice in experiment. The results can provide the data support for the superconductivity research and experimental synthesis of hydrides in Li-Y-H ternary system.