  We analyze the potential sensitivity of a search for $e\rightarrow\tau$
conversion at a proposed electron-ion collider (EIC) facility. To that end, we
calculate the cross sections for $e\rightarrow\tau$ events in a leptoquark
framework assuming that the leptoquark masses are on the order of several
hundred GeV or more. Given present limits on leptoquarks from direct searches
at HERA and rare decay processes, an EIC sensitive to 0.1 fb $e\rightarrow\tau$
cross sections could probe previously unexplored regions of parameter space for
these lepton flavor violating events (assuming 90 GeV center-of-mass energy and
10 fb$^{-1}$ integrated luminosity). Depending on the species of leptoquark and
flavor structure of the couplings, an EIC search could surpass the HERA and
rare process sensitivity to $e\rightarrow\tau$ conversion amplitudes by as much
as an order of magnitude or more. We also derive updated limits on quark
flavor-diagonal LFV leptoquark interactions using the most recent BaBar
$\tau\rightarrow e\gamma$ search. We find that limits from an EIC
$e\rightarrow\tau$ search could be competitive with the most recent
$\tau\rightarrow e\gamma$ limit for a subset of the quark flavor-diagonal
leptoquark couplings. Using an SU(5) GUT model in which leptoquark couplings
are constrained by the neutrino masses and mixing, we illustrate how observable
leptoquark-induced $e\rightarrow\tau$ conversion can be consistent with
stringent LFV limits imposed by $\mu\rightarrow e\gamma$ and $\mu\rightarrow e$
conversion searches.
