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We consider the lepton-flavor violating (LFV) lepton-quark dimension-6operators and analyze their contributions to the LFV leptonic decays of vector,pseudoscalar, and scalar neutral mesons $M\to \ell_1 \ell_2$ as well as to$\mu(\tau) \rightarrow \ell ee, \ell \gamma\gamma$ decays. These operatorscontribute to the purely leptonic processes via quark loop. On the basis ofquark-hadron duality, we relate these loops to the appropriate meson-exchangecontributions. In this way, we extract lower bounds on the individual scales ofthe studied LFV operators from the experimental and phenomenological limits onthe leptonic decays of mesons and leptons. As a byproduct, we shall obtain newlimits on the LFV leptonic decays of flavored mesons from the experimentalbounds on the three-body lepton decays. We study the effects of QED and QCDradiative corrections to the LFV lepton-quark operators in question. We derivefor them the one-loop matrix of the RGE evolution and examine its effect on thepreviously derived tree-level limits on these operators. We show that the QEDcorrections are particularly relevant due to operator mixing. Specifically, forsome of them the limits on their individual LFV scales improve by up to 3orders of magnitude.

RGE effects on the LFV scale from meson decays