Using e+e− collision data collected with the BESIII detector operating at the BEPCII collider, the Born cross sections of e+e−→Λc+Λ¯c(2595)−+c.c. and e+e−→Λc+Λ¯c(2625)−+c.c. are measured for the first time at center-of-mass energies of s=4918.0 and 4950.9 MeV. Nonzero cross sections are observed very close to the production threshold. The measured Born cross sections of e+e−→Λc+Λ¯c(2625)−+c.c. are about 2–3 times greater than those of e+e−→Λc+Λ¯c(2595)−+c.c., providing the similar behavior as semileptonic decays of Λb0, but different behavior from that in the hadronic decays of Λb0. The Born cross sections are 15.6±3.1±0.9 pb and 29.4±3.7±2.7 pb for e+e−→Λc+Λ¯c(2595)−+c.c., and are 43.4±4.0±4.1 pb and 76.8±6.5±4.2 pb for e+e−→Λc+Λ¯c(2625)−+c.c. at s=4918.0 and 4950.9 MeV, respectively. Based on the polar angle distributions of the Λ¯c(2625)− and Λc(2625)+, the form-factor ratios |GE|2+3|GM|2/|GC| are determined for e+e−→Λc+Λ¯c(2625)−+c.c. for the first time, which are 5.95±4.07±0.15 and 0.94±0.32±0.02 at s=4918.0 and 4950.9 MeV, respectively. All of these first uncertainties are statistical and second systematic. Published by the American Physical Society 2024