Lepton-flavor-violating (LFV) scalar portal is an interesting mechanism that connects the dark sector to the visible one. This mechanism leads to a rich phenomenology including an extra contribution to muon anomalous magnetic moment desirable for alleviating the discrepancy between the updated SM prediction and the combined results of Fermilab and BNL measurements. With the low-energy effective coupling ${{\cal L}_{\phi \mu e}} = - {y_{\mu e}}\left( {{{\bar e}_L}{\mu _R}\phi + {{\bar \mu }_R}{e_L}{\phi ^*}} \right)$, which turns muon into electron or vice versa through the scalar $\phi $, we derive the $\left( {{y_{\mu e}},{m_\phi }} \right)$ parameter space that could account for the discrepancy mentioned above. Furthermore, we calculate the cross section induced by ${{\cal L}_{\phi \mu e}}$ and SM vertices. Using Belle II model-independent $90\% $ C.L. upper limit on $\varepsilon ({\rm{efficiency}}) \times \sigma \left( {{e^ + }{e^ - } \to {e^ \pm }{\mu ^ \mp } + {\rm{invisible}}} \right)$ with ${\cal L}$ = 276 ${\rm{p}}{{\rm{b}}^{{\rm{ - 1}}}}$ [1], we obtain the corresponding upper limit for ${y_{\mu e}} \times \sqrt {\varepsilon .Br\left( {\phi \to {\rm{invisible}}} \right)} $ with $\varepsilon$ the signal efficiency. With the assumption of $Br\left( {\phi \to {\rm{invisible}}} \right) = 1$ and the implementation of ECL selection criteria for the signal reconstruction of processes ${{e^ + }{e^ - } \to {e^ \pm }{\mu ^ \mp }\phi }$, we found that for $0.5 \le {m_\phi } \le 8$ GeV, the sensitivity to ${y_{\mu e}}$ has not yet reached the favorable parameter range to account for the measured ${g_\mu } - 2$. We stress that explicit details of scalar portal models would determine $Br\left( {\phi \to {\rm{invisible}}} \right)$ while the detection efficiency requires a detailed experimental analysis. We point out that the search for ${e^ + }{e^ - } \to {e^ \pm }{\mu ^ \mp } + {\rm{invisible}}$ in Belle II is limited by the rather large rapidities (in absolute value) of final-state leptons. This indicates that the searches for similar processes induced by LFV scalar portal models in fixed-target experiments will be more promising.