Searches for lepton-flavor-violating decays of a τ lepton to a lighter mass lepton and a photon have been performed with the entire data set of (963±7)×106 τ decays collected by the BABAR detector near the Υ(4S), Υ(3S) and Υ(2S) resonances. The searches yield no evidence of signals and we set upper limits on the branching fractions of B(τ±→e±γ)<3.3×10-8 and B(τ±→μ±γ)<4.4×10-8 at 90% confidence level.