A simultaneous fit is performed to the $e^+e^-to Lambda_c^+Lambda_c^-$ cross section data measured by Belle and BESIII from threshold up to 5.4 GeV. In order to accommodate both the BESIII measurement near threshold and the Belle observation of a resonance $Y(4630)$, we build a composite PDF with a Breit-Wigner resonance and a continuum contribution to model the full cross section line shape of $e^+e^-to Lambda_c^+Lambda_c^-$. The fit gives a mass of $M=[4636.1_{-7.2}^{+9.8} ($stat$)pm 8.0($syst$)]$~MeV/$c^2$, a width of $Gamma_{rm tot}=[34.5_{-16.2}^{+21.0} ($stat$)pm 5.6($syst$)]$~MeV, and $Gamma_{e^+ e^-}mathcal{B}[Y(4630)toLambda_c^+Lambda_c^-]=[18.3_{-6.1}^{+8.8} ($stat$)pm 1.1($syst$)]$~eV/$c^2$ for the resonance. The width of $Y(4630)$ from our study is narrower than the previous Belle fit. The mass and width of $Y(4630)$ also show good agreement with a vector resonance $Y(4626)$ recently observed in $D_s^+D_{s1}(2536)^-$ by Belle.
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