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Abstract We presentslick(the Scalable Line Intensity Computation Kit), a software package that calculates realistic CO, [Ci], and [Cii] luminosities for clouds and galaxies formed in hydrodynamic simulations. Built on the radiative transfer codedespotic,slickcomputes the thermal, radiative, and statistical equilibrium in concentric zones of model clouds, based on their physical properties and individual environments. We validate our results by applyingslickto the high-resolution run of theSimbasimulations, testing the derived luminosities against empirical and theoretical/analytic relations. To simulate the line emission from a universe of emitting clouds, we have incorporated random forest machine learning (ML) methods into our approach, allowing us to predict cosmologically evolving properties of CO, [Ci], and [Cii] emission from galaxies such as luminosity functions. We tested this model in 100,000 gas particles, and 2500 galaxies, reaching an average accuracy of ∼99.8% for all lines. Finally, we present the first model light cones created with realistic and ML-predicted CO, [Ci], and [Cii] luminosities in cosmological hydrodynamical simulations, fromz= 0 toz= 10.