  We study charged lepton flavor violation associated with a light leptophilic
axion-like particle (ALP), $X$, at the $B$-factory experiment Belle II. We
focus on production of the ALP in the tau decays $\tau \to X l$ with $l=e,\mu$,
followed by its decay via $X\to l^- l^+$. The ALP can be either promptly
decaying or long-lived. We perform Monte-Carlo simulations, recasting a prompt
search at Belle for lepton-flavor-violating $\tau$ decays, and propose a
displaced-vertex (DV) search. For both types of searches, we derive the
Belle~II sensitivity reaches in both the product of branching fractions and the
ALP coupling constants, as functions of the ALP mass and lifetime. The results
show that the DV search exceeds the sensitivity reach of the prompt search to
the relevant branching fractions by up to about a factor of 40 in the long
decay length regime.
