  Future lepton colliders such as the CEPC and FCC-ee would run as
high-luminosity $Z-$boson factories, which offer a unique opportunity to study
long-lived particles which couple to Z-bosons. In order to exemplify this
particular advantage, in this work we consider one benchmark physics scenario
where the long-lived lightest neutralinos pair
$(\tilde{\chi}_1^0\tilde{\chi}_1^0)$ is produced from $Z-$decays in the context
of the R-parity violating supersymmetry. Our analysis indicates that when
assuming BR$(Z\rightarrow \tilde{\chi}_1^0\tilde{\chi}_1^0) = 10^{-3}$ and
$m_{\tilde{\chi}_1^0} \sim 40$ GeV, the model parameter $\lambda'_{112} /
m^2_{\tilde{f}}$ can be discovered down to as low as $\sim 1.5 \times 10^{-14}$
($3.9 \times 10^{-14}$) GeV$^{-2}$ at the FCC-ee (CEPC) with center-of-mass
energy $\sqrt{s} = 91.2$ GeV and 150 (16) ab$^{-1}$ integrated luminosity.
These limits exceed the projected sensitivity reaches of the ATLAS experiment
at the HL-LHC and the proposed LHC experiments with far detectors (AL3X,
CODEX-b, FASER, and MATHUSLA).
