Computational modeling of lipid ternary mixtures is challenging because of their complicated and segmented phase diagram, the long timescales required for mixing the system components, and the necessity to sufficiently sample the three-dimensional phase space. Here, we investigate a ternary system, which mimics the lipid matrix of the stratum corneum, the outermost layer of the epidermis and the primary barrier for transdermal drug absorption. Our system consists of ceramide, cholesterol, and lignoceric acid at 23 different composition ratios, which we study at two different temperatures using coarse-grained molecular dynamics (CG MD) simulations. As CG MD simulations heavily depend on the choice of parameters, first an improved set of ceramide CG parameters was developed that reproduces experimental and all-atom simulation data. Second, the performance of the recently updated MARTINI 2015 cholesterol force field was systematically evaluated and compared to the 2007 model. We provide a detailed analysis of the structural and dynamic properties of the ternary system, such as area per lipid, area compressibility modulus, lipid order parameters, bilayer thickness, lipid tail interdigitation, and lateral self-diffusion. Based on the analysis of these properties, we devise a phase diagram of the ternary system, where three different phases, namely, liquid-disordered, gel, and liquid-ordered, are observed. The individual occurrence of a certain phase not only depends on the component molar ratio and the temperature but also decisively on the employed cholesterol force field.