  We explore parameter space in the Zee Model to resolve the long-standing
tension of the electron and muon anomalous magnetic moment (AMM). The model
comprises a second Higgs doublet and a charged singlet at electroweak scale and
generates Majorana neutrino masses at one-loop level; the neutral partner of
the $SU(2)_L$ doublet contributes to the AMM of electron and muon via one loop
and two-loop corrections. We propose two minimal flavor structures that can
explain these anomalies while fitting the neutrino oscillation data. We find
that the neutral Higgs resides in the mass range of roughly 10-300 GeV or 1-30
GeV, depending on the flavor structures. The model is consistent with
constraints from colliders, electroweak precision data, and lepton flavor
violation. To be comprehensive, we examine the constraints from the electric
dipole moment (EDM) and find a region of parameter space that gives a sizable
contribution to muon EDM while simultaneously giving corrections to muon AMM.
In addition to the light scalar, the two charged scalars with masses as low as
100 GeV can induce nonstandard interactions $\varepsilon_{ee}$ as large as
$8\%$, potentially hinting at new physics. We also investigate the projected
capability of future lepton colliders to probe the currently allowed parameter
space consistent with both electron and muon AMMs via direct searches in the
$\ell^{+}\ell^{-}\to \ell^{+}\ell^{-}(H \to \ell^{+}\ell^{-})$ channel.
