  We present a complete analysis of Lepton Flavor Universality (LFU) violations
in leptonic $\tau$ decays in motivated models addressing the $B$-physics
anomalies, based on the $SU(4)\times SU(3)\times SU(2)\times U(1)$ gauge group.
We show that the inclusion of vector-like fermions, required by $B$-physics
data, leads to sizable modifications of the leading-log results derived within
an Effective Field Theory approach. In the motivated parameter-space region
relevant to the $B$-physics anomalies, the models predict a few per-mil
decrease of the effective $W$-boson coupling to $\tau$, within the reach of
future experiments.
