Abridged for arXiv: In this work, we apply a powerful new technique in order to observationally derive accurate assembly histories through a self-consistent combined stellar dynamical and population galaxy model. We present this approach for three edge-on lenticular galaxies from the Fornax3D project -- FCC 153, FCC 170, and FCC 177 -- in order to infer their mass assembly histories individually and in the context of the Fornax cluster. The method was tested on mock data from simulations to quantify its reliability. We find that the galaxies studied here have all been able to form dynamically-cold (intrinsic vertical velocity dispersion $sigma_z lesssim 50 {rm km} {rm s}^{-1}$) stellar disks after cluster infall. Moreover, the pre-existing (old) high angular momentum components have retained their angular momentum (orbital circularity $lambda_z > 0.8$) through to the present day. Comparing the derived assembly histories with a comparable galaxy in a low-density environment -- NGC 3115 -- we find evidence for cluster-driven suppression of stellar accretion and merging. We measured the intrinsic stellar age--velocity-dispersion relation and find that the shape of the relation is consistent with galaxies in the literature across redshift. There is tentative evidence for enhancement in the luminosity-weighted intrinsic vertical velocity dispersion due to the cluster environment. But importantly, there is an indication that metallicity may be a key driver of this relation. We finally speculate that the cluster environment is responsible for the S0 morphology of these galaxies via the gradual external perturbations, or `harassment, generated within the cluster.
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