  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. 
Lower bounds on lepton flavor violating branching ratios in a radiative   seesaw model