\begin{document}$ \Lambda\bar{\Lambda} $\end{document} decay"> \begin{document}$ e^+e^-\rightarrow \Lambda\bar{\Lambda} $\end{document}, we calculate the mass spectrum of the \begin{document}$ \phi $\end{document} meson with the GI model. For the excited vector strangeonium states \begin{document}$ \phi(3S,\; 4S,\; 5S,\; 6S) $\end{document} and \begin{document}$ \phi(2D,\; 3D,\; 4D,\; 5D) $\end{document}, we investigate the electronic decay width with the Van Royen-Weisskopf formula, and the partial widths of the \begin{document}$ \Lambda\bar{\Lambda} $\end{document}, \begin{document}$ \Xi^{-(*)}\bar{\Xi}^+ $\end{document}, and \begin{document}$ \Sigma^{+(*)}\bar{\Sigma}^{-(*)} $\end{document} decay modes with the extended quark-pair creation model. We find that the electronic decay width of the \begin{document}$ D $\end{document}-wave vector strangeonium is about \begin{document}$ 3\sim8 $\end{document} times larger than of the \begin{document}$ S $\end{document}-wave vector strangeonium. Around 2232 MeV, the partial decay width of the \begin{document}$ \Lambda\bar{\Lambda} $\end{document} mode can be up to several MeV for \begin{document}$ \phi(3^3S_1) $\end{document}, while the partial \begin{document}$ \Lambda\bar{\Lambda} $\end{document} decay width of \begin{document}$ \phi(2^3D_1) $\end{document} is \begin{document}$ {\cal{O}}(10^{-3}) $\end{document} keV. If the threshold enhancement reported by the BESIII collaboration arises from the strangeonium meson, this state is very likely the \begin{document}$ \phi(3^3S_1) $\end{document} state. We also note that the \begin{document}$ \Lambda\bar{\Lambda} $\end{document} and \begin{document}$ \Sigma^{+}\bar{\Sigma}^{-} $\end{document} partial decay widths of the states \begin{document}$ \phi(3^3D_1) $\end{document} and \begin{document}$ \phi(4^3S_1) $\end{document} are several MeV, which is sufficient to be observed in future experiments."> A possible explanation of the threshold enhancement in the process <inline-formula><tex-math id="M1">\begin{document}$ {{e^+e^-\rightarrow \Lambda\bar{\Lambda} }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/cpc/article/app/id/ccdb4364-0b2d-4e27-87f5-d65193fd34fb/CPC-2019-0207_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/cpc/article/app/id/ccdb4364-0b2d-4e27-87f5-d65193fd34fb/CPC-2019-0207_M1.png"/></alternatives></inline-formula> -
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