We report the first measurement of the absolute branching fraction for Lambda(+)(c) -> Lambda e(+)nu(e). This measurement is based on 567 pb(-1) of e(+)e(-) annihilation data produced at root s = 4.599 GeV, which is just above the Lambda(+)(c)Lambda(-)(c) threshold. The data were collected with the BESIII detector at the BEPCII storage rings. The branching fraction is determined to be B(Lambda(+)(c) -> Lambda e(+)nu(e)) = [3.63 +/- 0.38(stat) +/- 0.20(syst)] %, representing a significant improvement in precision over the current indirect determination. As the branching fraction for Lambda(+)(c) -> Lambda e(+)nu(e) is the benchmark for those of other Lambda(+)(c) semileptonic channels, our result provides a unique test of different theoretical models, which is the most stringent to date.