  Lepton flavor violation (LFV), observed conclusively in neutrino
oscillations, remains a pivotal area of investigation due to its absence in the
Standard Model (SM). Beyond the Standard Model (BSM) physics explores charged
lepton flavor violation (CLFV), particularly through new particle candidates
such as the $Z^{'}$. This article focuses on maximal LFV interactions
facilitated by the $Z^{'}$ boson, specifically targeting its off-diagonal
interactions with the first and second generations of charged and neutral
leptons. In our ultraviolet (UV) model for the origin of the $Z^{'}$, inspired
by the work of [R.Foot \textit{et al.,}~arxiv:hep-ph/9401250], we utilize the
discrete $Z_2$ symmetry to investigate the maximal LFV mediated by the $Z^{'}$
between the muon ($\mu$) and electron ($e$) arising from the additional
scalars. This symmetry prohibits flavor-conserving interactions between $Z'$
and $\mu^+\mu^-,\, e^+e^-$. In conjunction with collider, $(g-2)_{\mu},
(g-2)_e$, inverse $\mu$ decay and LFV decay constraints, we provide forecasts
for anticipated limits derived from processes such as $\nu_\mu N \to \nu_e
\mu^+ e^- N$ in neutrino trident experiments like the DUNE experiment. These
limits highlight the prospective scope and significance of LFV investigations
within these experimental frameworks. From the range of mass between 0.01 GeV
and 10 GeV, the most stringent limit arise from $ \textit{B} (\mu \to e + X
+\gamma)$ for $M_{Z^{'}} < m_\mu$ while neutrino trident processes constrain
effectively as $M_{Z^{'}} \to 10$ GeV.
