We study an extension of the minimal gauged Lμ-Lτ model including three right-handed singlet fermions and a scalar doublet to explain the anomalous magnetic moments of muon and electron simultaneously. The presence of an in-built Z2 symmetry under which the right-handed singlet fermions and η are odd, gives rise to a stable dark matter candidate along with light neutrino mass in a scotogenic fashion. In spite of the possibility of having positive and negative contributions to muon and electron (g-2) respectively from vector boson and charged scalar loops, the minimal scotogenic Lμ-Lτ model cannot explain both muon and electron (g-2) simultaneously while being consistent with other experimental bounds. We then extend the model with a vectorlike lepton doublet which not only leads to a chirally enhanced negative contribution to electron (g-2) but also leads to the popular singlet-doublet fermion dark matter scenario. With this extension, the model can explain both electron and muon (g-2) while being consistent with neutrino mass, dark matter and other direct search bounds. The model remains predictive at high energy experiments like collider as well as low energy experiments looking for charged lepton flavor violation, dark photon searches, in addition to future (g-2) measurements. © 2022 authors. Published by the American Physical Society.