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We explore the potential to detect the U ( 1 ) L μ − L τ model featuring triplet scalars Δ at the μ TRISTAN collider. The new gauge boson Z ′, arising from the spontaneous breaking of U ( 1 ) L μ − L τ , can exhibit maximal flavor changing interactions under the exchange symmetry, while Δ mediates the flavor conserving interactions. The absence of muon ( g − 2 ) μ can be explained by interference effects arising from opposite contributions of Z ′ and Δ, with similar interference patterns also manifesting in the tau decay process τ → μ ν ν ¯ . These counteracting effects render the model phenomenologically interesting and warrant further investigation. For the mass m Z ′ in the range of hundreds of GeV, we find that μ + μ + and μ + e − collider at the μ TRISTAN can probe many regions inaccessible to current experiments and offer greater projected sensitivity than opposite-sign muon colliders. This suggests that μ TRISTAN can serve as complementary exploration to the U ( 1 ) L μ − L τ model, providing compelling motivation for the next generation of high-energy lepton colliders.