  Taking into account the constraints on the lepton flavor violation (LFV)
couplings of the Standard Model (SM) Higgs boson H with leptons from low energy
experiments and the recent Compact Muon Solenoid experiment results, we
investigate production of the SM Higgs boson associated with a lepton \tau via
e \gamma collision at the International Linear Collider (ILC) and Large Hadron
Electron Collider experiments. The production cross sections are calculated and
the LFV signals and the relevant SM backgrounds are examined. The LFV signals
of the SM Higgs boson might be observed via e \gamma collision in future ILC
experiments.
