Observation of ${\chi }_{cJ}\to \mathrm{\Lambda }{K}_S^0{\bar{\mathrm{\Xi }}}^0+c\mathrm{.}c\mathrm{.}$ and improved measurements of ${\chi }_{cJ}\to \mathrm{\Lambda }{K}^{-}{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.}$

By analyzing $(2712.4\pm 14.3)\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector operating at the BEPCII collider, we report the first observation of ${\chi }_{cJ}\to \mathrm{\Lambda }{K}_S^0{\bar{\mathrm{\Xi }}}^0+c\mathrm{.}c\mathrm{.}$ ($J=0,1,2$) with significances greater than $10\sigma$, including systematic uncertainties, and improved measurements of ${\chi }_{cJ}\to \mathrm{\Lambda }{K}^{-}{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.}$ The branching fractions of these decays are determined to be $\mathcal{B}({\chi }_{c0}\to \mathrm{\Lambda }{K}_S^0{\bar{\mathrm{\Xi }}}^0+c\mathrm{.}c\mathrm{.})=(1.13\pm 0.13\pm 0.13)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c1}\to \mathrm{\Lambda }{K}_S^0{\bar{\mathrm{\Xi }}}^0+c\mathrm{.}c\mathrm{.})=(0.74\pm 0.08\pm 0.07)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c2}\to \mathrm{\Lambda }{K}_S^0{\bar{\mathrm{\Xi }}}^0+c\mathrm{.}c\mathrm{.})=(1.16\pm 0.11\pm 0.14)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c0}\to \mathrm{\Lambda }{K}^{-}{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.})=(1.90\pm 0.08\pm 0.16)\times {10}^{-4}$, $\mathcal{B}({\chi }_{c1}\to \mathrm{\Lambda }{K}^{-}{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.})=(1.40\pm 0.05\pm 0.11)\times {10}^{-4}$, and $\mathcal{B}({\chi }_{c2}\to \mathrm{\Lambda }{K}^{-}{\bar{\mathrm{\Xi }}}^{+}+c\mathrm{.}c\mathrm{.})=(1.95\pm 0.07\pm 0.15)\times {10}^{-4}$. The first uncertainties are statistical, and the second are systematic.