  Over the last decade, conflicting values of the hypertriton
${}_{\Lambda}^3\mathrm{H}$ lifetime $\tau({}_{\Lambda}^3\mathrm{H})$ were
extracted from relativistic heavy-ion (RHI) collision experiments, ranging from
values compatible with the free-$\Lambda$ lifetime $\tau_\Lambda$-as expected
naively for a very weakly bound $\Lambda$ in ${}_{\Lambda}^3\mathrm{H}$-to
lifetimes as short as $\tau({}_{\Lambda}^3\mathrm{H}) \approx
(0.4-0.7)\,\tau_\Lambda$. In a recent work [Phys. Lett. B 811, 135916 (2020)]
we studied this ${}_{\Lambda}^3\mathrm{H}$ lifetime puzzle theoretically using
realistic three-body ${}_{\Lambda}^3\mathrm{H}$ and ${}^3\mathrm{He}$ wave
functions computed within the ab initio no-core shell model approach with
interactions derived from chiral effective field theory. In particular,
$\tau({}_{\Lambda}^3\mathrm{H})$ was found to be strongly correlated with the
$\Lambda$ separation energy $B_\Lambda$ in ${}_{\Lambda}^3\mathrm{H}$, the
value of which is rather poorly known experimentally and, in addition, is known
to suffer from sizable theoretical uncertainties inherent in the employed
nuclear and hypernuclear interaction models. In the present work we find that
these uncertainties propagate into $\tau({}_{\Lambda}^3\mathrm{H})$, and thus
limit considerably the theoretical precision of its computed value. Although
none of the conflicting RHI measured $\tau({}_{\Lambda}^3\mathrm{H})$ values
can be excluded, but rather can be attributed to a poor knowledge of
$B_\Lambda$, we note the good agreement between the lifetime value
$\tau({}_{\Lambda}^3\mathrm{H})=238(27)$ ps computed at the lowest value
$B_\Lambda=66$ keV reached by us and the very recent ALICE measured lifetime
value $\tau^{\mathrm{ALICE}}({}_{\Lambda}^3\mathrm{H})=253(11)(6)$ ps
associated with the ALICE measured $B_\Lambda$ value
$B^{\mathrm{ALICE}}_\Lambda=102(63)(67)$ keV [Phys. Rev. Lett. 131, 102302
(2023)].
