  Recent $_\Lambda^3$H lifetime measurements in relativistic heavy ion
collision experiments have yielded values shorter by (30$\pm$8)% than the free
$\Lambda$ lifetime $\tau_\Lambda$, thereby questioning the naive expectation
that $\tau({_\Lambda^3}{\rm H})\approx\tau_\Lambda$ for a weakly bound
$\Lambda$ hyperon. Here we apply the closure approximation introduced by Dalitz
and coworkers to evaluate the $_\Lambda^3$H lifetime, using $_\Lambda^3$H
wavefunctions generated by solving three-body Faddeev equations. Our result,
disregarding pion final-state interaction (FSI), is $\tau({_\Lambda^3}{\rm
H})$=(0.90$\pm$0.01)$\tau_\Lambda$. In contrast to previous works, pion FSI is
found attractive, reducing further $\tau({_\Lambda^3}{\rm H})$ to
$\tau({_\Lambda^3}{\rm H})$=(0.81$\pm$0.02)$\tau_\Lambda$. We also evaluate for
the first time $\tau({_\Lambda^3}{\rm n})$, finding it considerably longer than
$\tau_\Lambda$, contrary to the shorter lifetime values suggested by the GSI
HypHI experiment for this controversial hypernucleus.
