The cross section of the e(+)e(-) -> Lambda(+)(c)(Lambda) over bar (-)(c) process is measured with unprecedented precision using data collected with the BESIII detector at root s = 4574.5, 4580.0, 4590.0 and 4599.5 MeV. The nonzero cross section near the Lambda(+)(c)(Lambda) over bar (-)(c) production threshold is cleared. At center-of-mass energies root s = 4574.5 and 4599.5 MeV, the higher statistics data enable us to measure the Lambda(c) polar angle distributions. From these, the.c electric over magnetic form-factor ratios (vertical bar G(E)/G(M)vertical bar) 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.