  We study a simple left-right symmetric (LRS) extension of the Zee model for
neutrino mass generation. An extra $SU(2)_{L/R}$ singlet charged scalar helps
in generating a loop-induced Majorana mass for neutrinos in this model. The
right-handed neutrinos in this case are very light of the order of a few eV to
a few MeV which makes this scenario quite different from other LRS models. We
have analyzed the scalar potential and Higgs spectrum in detail, which also
play an important role for the neutrino phenomenology. We identified the
parameter regions in the model which satisfy the experimentally observed
neutrino masses and mixings along with other experimental constraints. We have
then studied the collider signatures of the charged scalar at $e^+e^-$
colliders with different benchmark points. It is possible to get a huge
enhancement in the production cross-section of the charged scalar at lepton
collider compared to the hadron colliders, resulting in a much stronger signal
which can be easily observed at the upcoming ILC or CLIC experiments.
