  We consider the lepton-flavor violating (LFV) lepton-quark dimension-6
operators 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 operators
contribute to the purely leptonic processes via quark loop. On the basis of
quark-hadron duality, we relate these loops to the appropriate meson-exchange
contributions. In this way, we extract lower bounds on the individual scales of
the studied LFV operators from the experimental and phenomenological limits on
the leptonic decays of mesons and leptons. As a byproduct, we shall obtain new
limits on the LFV leptonic decays of flavored mesons from the experimental
bounds on the three-body lepton decays. We study the effects of QED and QCD
radiative corrections to the LFV lepton-quark operators in question. We derive
for them the one-loop matrix of the RGE evolution and examine its effect on the
previously derived tree-level limits on these operators. We show that the QED
corrections are particularly relevant due to operator mixing. Specifically, for
some of them the limits on their individual LFV scales improve by up to 3
orders of magnitude.
