We report the first measurements of absolute branching fractions for the $W$-exchange-only processes $Lambda^+_ctoXi^0K^+$ and $Lambda^+_ctoXi(1530)^0K^+$ with the double-tag technique, by analyzing an $e^{+}e^{-}$ collision data sample, that corresponds to an integrated luminosity of 567 pb$^{-1}$ collected at a center-of-mass energy of 4.6 GeV by the BESIII detector. The branching fractions are measured to be $mathcal{B}(Lambda^+_ctoXi^0K^+)=(5.90pm0.86pm0.39)times10^{-3}$ and $mathcal{B}(Lambda^+_ctoXi(1530)^0K^+)=(5.02pm0.99pm0.31)times10^{-3}$, where the first uncertainties are statistical and the second systematic. Our results are more precise than the previous relative measurements.
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