  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
$\Gamma_{e^+
e^-}\mathcal{B}[Y(4630)\to\Lambda_c^+\Lambda_c^-]=[18.3_{-6.1}^{+8.8}
($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.
