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Using $e^+e^-$ collision data collected with the BESIII detector operating atthe BEPCII collider, the Born cross sections of $e^+e^-\to \Lambda_{c}^+\bar{\Lambda}_{c}(2595)^- + \rm{c.c.}$ and $e^+e^-\to \Lambda_{c}^+\bar{\Lambda}_{c}(2625)^- + \rm{c.c.}$ are measured for the first time atcenter-of-mass energies of $\sqrt{s}=4918.0$ and 4950.9 MeV. Non-zero crosssections are observed very close to the production threshold. The measured Borncross sections of $e^+e^-\to \Lambda_{c}^+ \bar{\Lambda}_{c}(2625)^- +\rm{c.c.}$ are about $2\sim3$ times greater than those of $e^+e^-\to\Lambda_{c}^+ \bar{\Lambda}_{c}(2595)^- + \rm{c.c.}$, thereby indicating thatthe exotic structure potentially exists in the excited charmed baryons. TheBorn cross sections are $15.6\pm3.1\pm0.9$ pb and $29.4\pm3.7\pm2.7$ pb for$e^+e^-\to \Lambda_{c}^+ \bar{\Lambda}_{c}(2595)^- + \rm{c.c.}$, and are$43.4\pm4.0\pm4.1$ pb and $76.8\pm6.5\pm4.2$ pb for $e^+e^-\to \Lambda_{c}^+\bar{\Lambda}_{c}(2625)^- +\rm{c.c.}$ at $\sqrt s=4918.0$ and 4950.9 MeV,respectively. Based on the polar angle distributions of the$\bar{\Lambda}_{c}(2625)^-$ and $\Lambda_{c}(2625)^+$, the form-factor ratios$\sqrt{|G_{E}|^2 + 3|G_{M}|^2}/|G_{C}|$ are determined for $e^+e^-\to\Lambda_{c}^+ \bar{\Lambda}_{c}(2625)^- + \rm{c.c.}$ for the first time, whichare $5.95\pm4.07\pm0.15$ and $0.94\pm0.32\pm0.02$ at $\sqrt s=4918.0$ and4950.9 MeV, respectively. All of these first uncertainties are statistical andsecond systematic.

Measurements of Born Cross Sections for $e^+e^-\to \Lambda_{c}^+  \bar{\Lambda}_{c}(2595)^- + {\rm c.c.}$ and $e^+e^-\to \Lambda_{c}^+  \bar{\Lambda}_{c}(2625)^- + {\rm c.c.}$ at $\sqrt{s}=$4918.0 and 4950.9 MeV