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We introduce Isotonic Conditional Laws (ICL) which extend the classicalnotion of conditional laws by the additional requirement that there exists anisotonic relationship between the random variable of interest and theconditioning random object. We show existence and uniqueness of ICL building onconditional expectations given $\sigma$-lattices. ICL corresponds to aclassical conditional law if and only if the latter is already isotonic. ICL ismotivated from a statistical point of view by showing that ICL emergesequivalently as the minimizer of an expected score where the scoring rule maybe taken from a large class comprising the Continuous Ranked Probability Score(CRPS). Furthermore, ICL is calibrated in the sense that it is invariant tocertain conditioning operations, and the corresponding event probabilities andquantiles are simultaneously optimal with respect to all relevant scoringfunctions. We will develop a new notion of general conditional functionalsgiven $\sigma$-lattices which is of independent interest.