  We study the lepton flavor violating decays such as $\mu\to e\gamma$,
$\tau\to e\gamma$, $\tau\to \mu\gamma$ in the three-loop radiative seesaw model
proposed by Krauss, Nasri, and Trodden. In this model, the relevant coupling
constants are larger for the heavier scalars that run inside loop diagrams to
generate the appropriate magnitude of neutrino masses. Imposing a criterion
that all the coupling constants must be small enough to be treated
perturbatively, we find an upper bound on the mass of one of the scalars. By
combining it with neutrino mass parameters, we derive lower bounds on the
branching ratios of the lepton flavor violating processes. In a case with the
inverted mass ordering and best-fit neutrino oscillation parameters, one of the
lower bounds is $\text{Br}(\mu\to e\gamma)>1.1\times 10^{-13}$, which is within
the reach of the MEG~II experiment.
