Kinematics restricts the ability of rare charm decays to explore the charged lepton-flavor-violation processes mediated by the quark-level c -> ul tau transition. To fill the gap, we propose exploring new physics (NP) through the quasielastic scattering process e-p -> tau- Lambda c and the polarization of the tau lepton. As analyzing modes for the tau polarization, we consider the decays tau- -> pi- nu tau, tau- -> rho- nu tau, and tau- -> l-nul nu tau, and show that the tau polarization components can be extracted from analyzing the kinematics of the tau visible decay products. In the framewo...