We have studied the Tamm-type surface state of La(0001) by tunneling spectroscopy within a wide range of tunneling currents from 0.1 nA to 8000 nA, thereby tuning the electric-field strength in a tip-vacuum-sample tunnel junction. We observe a significant shift of the unoccupied Tamm-type surface state toward the Fermi energy with increasing electric-field strength, accompanied by a broadening of the width of the resonance peak indicating a decrease of the surface-state lifetime. Our experimental results are contrary to previous reports for Stark-shifted Shockley-type surface states of noble metal (111) surfaces.