  Using an $e^+ e^-$ collision data sample of $(10087 \pm 44)\times10^6
~J/\psi$ events taken at the center-of-mass energy of $3.097~\rm{GeV}$ by the
BESIII detector at the BEPCII collider, the process $\Lambda+N \rightarrow
\Sigma^+ + X$ is studied for the first time employing a novel method. The
$\Sigma^{+}$ hyperons are produced by the collisions of $\Lambda$ hyperons from
$J/\psi$ decays with nuclei in the material of the BESIII detector. The total
cross section of $\Lambda + ^{9}{\rm Be} \rightarrow \Sigma^+ + X$ is measured
to be $\sigma = (37.3 \pm 4.7 \pm 3.5)~{\rm mb}$ at $\Lambda$ beam momenta
within $[1.057, 1.091]~{\rm GeV}/c$, where the uncertainties are statistical
and systematic, respectively. This analysis is the first study of
$\Lambda$-nucleon interactions at an $e^+ e^-$ collider, providing information
and constraints relevant for the strong-interaction potential, the origin of
color confinement, the unified model for baryon-baryon interactions, and the
internal structure of neutron stars.
