Mesoscopic models are widely used to study complex organization and transport phenomena in chemical and biological systems. Defining a rigorous procedure by which a mesoscopic coarse-grained (CG) representation for a fluid can be constructed from an atomistic fine-grained (FG) model is a long-standing question in the field. The connection of these CG models with the FG level of description, which might be built by CG mappings from the FG model, is often unclear. The present paper introduces a new CG mapping scheme that uses dynamically self-consistent smooth centroidal Voronoi tessellation to address this challenging problem. The new mapping scheme is applied to the coarse-graining of supercritical Lennard-Jones fluid systems at different CG resolutions under both quiescent conditions and non-equilibrium shear flow. The method generates continuous, stable, and ergodic CG trajectories and quantitatively captures the slow collective motions of the underlying FG fluids. A parameterization of the CG models from the mapped CG trajectory is then developed based on the Mori-Zwanzig formalism. The Generalized Langevin Equation describes the dynamics of CG variables, and the parameterized result is shown to reproduce the structural and dynamical correlations of the CG system. The new dynamical mapping scheme and the parameterization protocol open up an avenue for direct bottom-up construction of mesoscopic models of fluids in a Lagrangian description.