  We address the question whether a violation of Lorentz symmetry can explain
the tension between the measurement and the Standard-Model prediction of the
anomalous magnetic moment of the muon ($(g-2)_{\mu}$) and whether it can
significantly impact the one of the electron ($(g-2)_{e}$). While anisotropic
Lorentz-violating effects are, in general, expected to produce sidereal
oscillations in observables, isotropic Lorentz violation in the charged-lepton
sector could feed into $(g-2)_{e,\mu}$. However, we find that this type of
Lorentz violation, parametrised via a dim-4 field operator of the
Standard-Model Extension (SME), is already strongly constrained by the absence
of vacuum \v{C}erenkov radiation and photon decay. In particular, the
observations of very-high-energetic astrophysical photons at LHAASO and of
high-energetic electrons (muons) by the LHC (IceCube) place the most stringent
two-sided bounds on the relevant SME coefficients $\overset{\circ}{c}{}^{(e)}$
($\overset{\circ}{c}{}^{(\mu)}$). Therefore, any explanation of the tension in
$(g-2)_{\mu}$ via isotropic Lorentz violation of the minimal spin-degenerate
SME is excluded, and the possible size of its impact on $(g-2)_{e}$ is very
limited.
