The cross section of the e^{+}e^{-}→Λ_{c}^{+}Λ[over ¯]_{c}^{-} process is measured with unprecedented precision using data collected with the BESIII detector at sqrt[s]=4574.5, 4580.0, 4590.0 and 4599.5 MeV. The nonzero cross section near the Λ_{c}^{+}Λ[over ¯]_{c}^{-} production threshold is cleared. At center-of-mass energies sqrt[s]=4574.5 and 4599.5 MeV, the higher statistics data enable us to measure the Λ_{c} polar angle distributions. From these, the Λ_{c} electric over magnetic form-factor ratios (|G_{E}/G_{M}|) 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.