The process e(+)e(-) -> Lambda(Lambda) over bar is studied using data samples at root s = 2.2324, 2.400, 2.800 and 3.080 GeV collected with the BESIII detector operating at the BEPCII collider. The Born cross section is measured at root s = 2.2324 GeV, which is 1.0 MeVabove the Lambda(Lambda) over bar mass threshold, to be 305 +/- 45(-36)(+66) pb, where the first uncertainty is statistical and the second systematic. The cross section near threshold is larger than that expected from theory, which predicts the cross section to vanish at threshold. The Born cross sections at root s = 2.400, 2.800 and 3.080 GeV are measured and found to be consistent with previous experimental results, but with improved precision. Finally, the corresponding effective electromagnetic form factors of Lambda are deduced.