  We present a lattice calculation of the Hadronic Vacuum Polarization (HVP)
contribution to the anomalous magnetic moments of the electron, $a_e^{\rm
HVP}$, the muon, $a_\mu^{\rm HVP}$, and the tau, $a_\tau^{\rm HVP}$, including
both the isospin-symmetric QCD term and the leading-order strong and
electromagnetic isospin-breaking corrections. Moreover, the contribution to
$a_\mu^{\rm HVP}$ not covered by the MUonE experimen, $a_{MUonE}^{\rm HVP}$, is
provided. We get $a_e^{\rm HVP} = 185.8~(4.2) \cdot 10^{-14}$, $a_\mu^{\rm HVP}
= 692.1~(16.3) \cdot 10^{-10}$, $a_\tau^{\rm HVP} = 335.9~(6.9) \cdot 10^{-8}$
and $a_{MUonE}^{\rm HVP} = 91.6~(2.0) \cdot 10^{-10}$. Our results are obtained
in the quenched-QED approximation using the QCD gauge configurations generated
by the European (now Extended) Twisted Mass Collaboration (ETMC) with
$N_f=2+1+1$ dynamical quarks, at three values of the lattice spacing varying
from $0.089$ to $0.062$ fm, at several values of the lattice spatial size ($L
\simeq 1.8 \div 3.5$ fm) and with pion masses in the range between $\simeq 220$
and $\simeq 490$ MeV.
