We explore the feasibility of using TeV-energy muons to probe lepton-flavor-violating (LFV) processes mediated by an axionlike particle (ALP) a with mass O(10 GeV). We focus on μτ LFV interactions and assume that the ALP is coupled to a dark state χ, which can be either less or more massive than a. Such a setup is demonstrated to be consistent with χ being a candidate for dark matter, in the experimentally relevant regime of parameters. We consider the currently operating NA64-μ experiment and proposed FASERν2 detector as both the target and the detector for the process μA→τAa, where A is the target nucleus. We also show that a possible future active muon fixed-target experiment operating at a 3 TeV muon collider or in its preparatory phase can provide an impressive reach for the LFV process considered, with future FASERν2 data providing a pilot study towards that goal. The implications of the muon anomalous magnetic moment (g−2)μ measurements for the underlying model, in case of a positive signal, are also examined, and a sample UV completion is outlined. Published by the American Physical Society 2024