  New physics scenarios beyond the Standard Model (SM) for neutrino mass
mechanism often necessitate the existence of a neutral scalar $H$ and/or
doubly-charged scalar $H^{\pm\pm}$, which couple to the SM charged leptons in a
flavor violating way, while evading all existing constraints. Such scalars
could be effectively produced at future lepton colliders like CEPC, ILC, FCC-ee
and CLIC, either on-shell or off-shell, and induce striking charged lepton
flavor violating (LFV) signals. We find that a large parameter space of the
scalar masses and the LFV couplings can be probed at lepton colliders, well
beyond the current low-energy constraints in the lepton sector. The neutral
scalar explanation of the muon $g-2$ anomaly could also be directly tested.
