  Motivated by the latest report on a high-$T_c$ family of La-Y ternary
hydrides (e.g., $P{\bar{1}}$-La$_2$YH$_{12}$, $Pm{\bar{3}}m$-LaYH$_{12}$, and
$Pm{\bar{3}}m$-(La,Y)H$_{10}$ with a maximum $T_c \sim 253$ K),[D. V. Semenok,
$et$ $al.$, arXiv preprint arXiv:2012.04787] we examined phase and structural
stabilities of a composite LaYH$_{12}$ using generic algorithm and ab initio
calculations to evaluate its pressure-dependent enthalpies for various
structural symmetries. In fact, based on the evaluation, the
$Pm\bar{3}m$-LaYH$_{12}$ reported in the previous study was found to be
unstable toward the decomposition into $R\bar{3}c$-LaH$_{6}$ +
$Im\bar{3}m$-YH$_{6}$. Instead of that, we found new crystal structures,
$R\bar{3}c$~(100-140 GPa) and $Cmmm$ clathrate phase~(140-300 GPa), being
stable against the decomposition. While $R\bar{3}c$ does not exhibit
superconductivity due to the extremely low density of states at the Fermi
level, $Cmmm$ phase is found to exhibit $T_{c}$ = 140.55~K at 200~GPa realized
by very high electron-phonon coupling constant ($\lambda$ = 1.876).
