  Motivated by the recent claim of hot superconductivity with critical
temperatures up to 550 K in La + x hydrides (arXiv:2006.03004), we investigate
the high-pressure phase diagram of possible compounds that may have formed in
the experiment, using first-principles calculations for evolutionary crystal
structure prediction and superconductivity. Starting from the hypothesis that
the observed T$_c$ may be realized by successive heating upon a pre-formed
LaH$_{10}$ phase, we examine plausible ternaries of lanthanum, hydrogen and
other elements present in the diamond anvil cell: boron, nitrogen, carbon,
platinum, gallium, gold. We find that only boron forms superhydride-like
structures that can host high-Tc superconductivity, but the predicted Tc are
incompatibe with the experimental reports. Our results indicate that, while the
claims of hot superconductivity should be reconsidered, it is very likely that
unkwown H-rich ternary or multinary phases containing lanthanum, boron and
hydrogen may have formed under the reported experimental conditions, and that
these may exhibit superconducting properties comparable, or even superior, to
those of currently known hydrides.
