The Born cross section of the $e^{+}e^{-}~rightarrow~Lambda_{c}^{+} bar{Lambda}_{c}^{-}$ process is measured with unprecedented precision using data collected with the BESIII detector at $sqrt{s}=4574.5$, $45580.0$, $4590.0$ and $4599.5$ $mathrm{MeV}$. The non-zero cross section near the $Lambda_{c}^{+} bar{Lambda}_{c}^{-}$ production threshold is discerned. At center-of-mass energies $sqrt{s}=4574.5$ and $4599.5 $ $mathrm{MeV}$, the higher statistics data enable us to measure the $Lambda_{c}$ polar angle distributions. From these, the ratio between the $Lambda_{c}$ electric and magnetic form factors ($|G_{E}/G_{M}|$) is measured for the first time. They are found to be $1.14pm0.14pm0.07$ and $1.23pm0.05pm0.03$ respectively, where the first uncertainties are statistical and the second are systematic.