  Motivated by the recent muon $g-2$ data, we study the lepton flavor violating
$l \to l' \gamma$ and $Z \to l \bar l'$ ($l, l' = e, \mu, \tau$) decays with $l
\neq l'$ in a scalar leptoquark model. Leptoquarks can produce sizable LFV
$l\to l'\gamma$ decay rates that can be easily reached by present or near
future experiments. % Leptoquark masses and couplings are constrained by the
muon $g-2$ data and the current $l \to l' \gamma$ bounds. We predict $Br(Z \to
\tau^\mp e^\pm)$ reaching the present limit ($10^{-5}$) and $Br(Z \to \mu^\mp
\tau^\pm)$ reaching $2\times 10^{-8}$, which will be accessible by future
linear colliders, whereas, the current bounds on LFV impose very strong
constraints on the $Br(Z \to \mu^\mp e^\pm)$ and the ratio is too low to be
observed in the near future.
