  The tiny neutrino masses measured in the neutrino oscillation experiments can
be naturally explained by the supersymmetric see-saw mechanism. If the
supersymmetry breaking is mediated by gravity, the see-saw models may predict
observable lepton flavor violating effects. In this work, we investigate the
lepton flavor violating process $\mu\to e\gamma$ in the kind of neutrino mass
models based on the idea of the ``lopsided'' form of the charged lepton mass
matrix. The constraints set by the muon anomalous magnetic moment are taken
into account. We find the present models generally predict a much larger
branching ratio of $\mu\to e\gamma$ than the experimental limit. Conversely,
this process may give strong constraint on the lepton flavor structure.
Following this constraint we then find a new kind of the charged lepton mass
matrix. The feature of the structure is that both the elements between the 2-3
and 1-3 generations are ``lopsided''. This structure produces a very small 1-3
mixing and a large 1-2 mixing in the charged lepton sector, which naturally
leads to small $Br(\mu\to e\gamma)$ and the LMA solution for the solar neutrino
problem.
