The cross section of the e+e-→Λc+Λc- process is measured with unprecedented precision using data collected with the BESIII detector at s=4574.5, 4580.0, 4590.0 and 4599.5 MeV. The nonzero cross section near the Λc+Λc- production threshold is cleared. At center-of-mass energies s=4574.5 and 4599.5 MeV, the higher statistics data enable us to measure the Λc polar angle distributions. From these, the Λc electric over magnetic form-factor ratios (|GE/GM|) are measured for the first time. They are found to be 1.14±0.14±0.07 and 1.23±0.05±0.03, respectively, where the first uncertainties are statistical and the second are systematic.