Measurements of $K_S^0$-$K_L^0$ asymmetries in the decays ${\mathrm{\Lambda }}_c^{+}\to p{K}_{L,S}^0$, $p{K}_{L,S}^0{\pi }^{+}{\pi }^{-}$ and $p{K}_{L,S}^0{\pi }^0$

Using $e^{+}{e}^{-}$ annihilation data sets corresponding to an integrated luminosity of 4.5 ${\text{fb}}^{-1}$, collected with the BESIII detector at center-of-mass energies between 4.600 and 4.699 GeV, we report the first measurements of the absolute branching fractions $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to p{K}_L^0)=(1.67\pm 0.06\pm 0.04)\mathrm{\%}$, $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to p{K}_L^0{\pi }^{+}{\pi }^{-})=(1.69\pm 0.10\pm 0.05)\mathrm{\%}$, and $\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to p{K}_L^0{\pi }^0)=(2.02\pm 0.13\pm 0.05)\mathrm{\%}$, where the first uncertainties are statistical and the second systematic. Combining with the known branching fractions of ${\mathrm{\Lambda }}_c^{+}\to p{K}_S^0$, ${\mathrm{\Lambda }}_c^{+}\to p{K}_S^0{\pi }^{+}{\pi }^{-}$, and ${\mathrm{\Lambda }}_c^{+}\to p{K}_S^0{\pi }^0$, we present the first measurements of the $K_S^0$-$K_L^0$ asymmetries $R({\mathrm{\Lambda }}_c^{+},K_{S,L}^{0}X)=\frac{\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to K_S^{0}X)-\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to K_L^{0}X)}{\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to K_S^{0}X)+\mathcal{B}({\mathrm{\Lambda }}_c^{+}\to K_L^{0}X)}$ in charmed baryon decays: $R({\mathrm{\Lambda }}_c^{+},p{K}_{S,L}^0)=-0.025\pm 0.031$, $R({\mathrm{\Lambda }}_c^{+},p{K}_{S,L}^0{\pi }^{+}{\pi }^{-})=-0.027\pm 0.048$, and $R({\mathrm{\Lambda }}_c^{+},p{K}_{S,L}^0{\pi }^0)=-0.015\pm 0.046$. No significant asymmetries within the uncertainties are observed.