  Axion-like particles (ALPs) arise in a variety of theoretical contexts and
can, in general, mediate flavor violating interactions and parity
non-conservation. We consider lepton flavor violating ALPs with GeV scale or
larger masses which may, for example, arise in composite dark sector models. We
show that a future Electron-Ion Collider (EIC) can uncover or constrain such
ALPs via processes of the type $e \, A_Z \to \tau \, A_Z\, a$, where $A_Z$ is a
nucleus of charge $Z$ and $a$ is an ALP in the range $m_\tau \leq m_a \lesssim
20$ GeV. The production of the ALP can have a large $Z^2$ enhancement from low
$Q^2$ electromagnetic scattering of the electron from a heavy ion. Using the
gold nucleus ($Z=79$) as an example, we show that the EIC can explore $e-\tau$
flavor violation, mediated by GeV-scale ALPs, well beyond current limits.
Importantly, the EIC reach for this interaction is not sensitive to the
lepton-flavor conserving ALP couplings, whose possible smallness can render
searches using $\tau$ decays ineffective. We also discuss how the EIC electron
beam polarization can provide a powerful tool for investigating parity
violating ALPs.
