  Several new physics scenarios that address anomalies in $B$-physics predict
an enhancement of $b \rightarrow s \tau \tau$ with respect to its Standard
Model prediction. Such scenarios necessarily imply modifications of the
lifetime ratio $\tau_{B_{s}}/\tau_{B_{d}}$ and the lifetime difference
$\Delta\Gamma_{s}$. In this work, we explore indirect bounds provided by these
observables over new physics scenarios. We also estimate future projections,
showing that future experimental and theoretical improvements on both
$\tau_{B_{s}}/\tau_{B_{d}}$ and $\Delta\Gamma_{s}$ have the potential to
provide bounds competitive with those directly extracted from $b\rightarrow s
\tau \tau$ transitions. After performing a model-independent analysis, we apply
our results to the particular case of leptoquark mediators proposed to address
the $R_{D^{(*)}}$ anomalies.
