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Using $1.31\times10^9$ $J/\psi$ events collected by the BESIII detector atthe Beijing Electron Positron Collider, we search for the process$J/\psi\to\Lambda_c^+e^-+c.c.$ for the first time. In this process, both baryonand lepton number conservation is violated. No signal is found and the upperlimit on the branching fraction $\mathcal{B}(J/\psi\to\Lambda_c^+e^-+c.c.)$ isset to be $6.9\times10^{-8}$ at the 90\% Confidence Level.

Search for Baryon and Lepton Number Violation in $J/\psi\to\Lambda_c^+e^-+c.c.$