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Based on $4.481\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\ensuremath{\psi}(3686)$ events collected with the BESIII detector at BEPCII, the branching fraction of the isospin violating decay $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}{\overline{\mathrm{\ensuremath{\Sigma}}}}^{0}\mathrm{\ensuremath{\Lambda}}+\mathrm{c}.\mathrm{c}.$ is measured to be $(1.60\ifmmode\pm\else\textpm\fi{}0.31\ifmmode\pm\else\textpm\fi{}0.13\ifmmode\pm\else\textpm\fi{}0.58)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, where the first uncertainty is statistical, the second is systematic, and the third is the uncertainty arising from interference with the continuum. This result is significantly smaller than the measurement based on CLEO-c data sets. The decays ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}}$ are measured via $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\chi}}_{cJ}$, and the branching fractions are determined to be $\mathcal{B}({\ensuremath{\chi}}_{c0}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}})=\phantom{\rule{0ex}{0ex}}(3.64\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\ensuremath{\chi}}_{c1}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}})=(1.31\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.06\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\ensuremath{\chi}}_{c2}\ensuremath{\rightarrow}\mathrm{\ensuremath{\Lambda}}\overline{\mathrm{\ensuremath{\Lambda}}})=\phantom{\rule{0ex}{0ex}}(1.91\ifmmode\pm\else\textpm\fi{}0.08\ifmmode\pm\else\textpm\fi{}0.17\ifmmode\pm\else\textpm\fi{}0.04)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, where the third uncertainties are systematic due to the $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\chi}}_{cJ}$ branching fractions.