We study the process e^{+}e^{-}→Λ_{c}^{+}Λ[over ¯]_{c}^{-} at twelve center-of-mass energies from 4.6119 to 4.9509 GeV using data samples collected by the BESIII detector at the BEPCII collider. The Born cross sections and effective form factors (|G_{eff}|) are determined with unprecedented precision after combining the single and double-tag methods based on the decay process Λ_{c}^{+}→pK^{-}π^{+}. Flat cross sections around 4.63 GeV are obtained and no indication of the resonant structure Y(4630), as reported by Belle, is found. In addition, no oscillatory behavior is discerned in the |G_{eff}| energy dependence of Λ_{c}^{+}, in contrast to what is seen for the proton and neutron cases. Analyzing the cross section together with the polar-angle distribution of the Λ_{c}^{+} baryon at each energy point, the moduli of electric and magnetic form factors (|G_{E}| and |G_{M}|) are extracted and separated. For the first time, the energy dependence of the form factor ratio |G_{E}/G_{M}| is observed, which can be well described by an oscillatory function.