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)_μ, 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 (LV) in the charged-lepton sector could also feed into (g — 2)_e,μ. 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 Čerenkov 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 c∘ ^(e) (c∘ ^(μ)). Therefore, any explanation of the tension in (g − 2)_μ 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.