Interest in searches for Charged Lepton Flavor Violation (CLFV) has continued in the past few decades since the observation of CLFV would indicate a new physics Beyond the Standard Model (BSM). As several future lepton colliders with high luminosity have been proposed, the search for CLFV will reach an unprecedented level of precision. Many BSM models allow CLFV processes at the tree level, such as the R-parity-violating (RPV) Minimal Supersymmetric Standard Model (MSSM), which is a good choice for benchmarking. In this paper, we perform a detailed fast Monte Carlo simulation study on RPV-induced CLFV processes at future lepton colliders, including a 240 GeV circular electron positron collider (CEPC) and a 6 or 14 TeV Muon Collider. As a result, we found that the upper limits on the τ-related RPV couplings will be significantly improved, while several new limits on RPV couplings can be set, which are inaccessible by low-energy experiments.