The compound-tunable embedding potential (CTEP) method developed in [Lomachuk et al., Phys. Chem. Chem. Phys., 2020, 22, 17922; Maltsev et al., Phys. Rev. B, 2021, 103, 205105] to describe the electronic structure of fragments and point defects in materials is applied to crystals containing periodically arranged lanthanide atoms, which can have an open 4f-shell. We consider YbF2, YbF3, YbCl2, and YbCl3 crystals for the pilot CTEP studies such that 4f-electrons are not treated explicitly at the CTEP generation stages. Instead, the pseudopotentials with 60 and 59 electrons in the core for Yb(II) and Yb(III), correspondingly, are applied and the latter treats the "4f-hole-in-core". At the final stage, the two-component embedded cluster study of fragments of YbHaln crystals (Hal = F, Cl; n = 2, 3) is performed using the CTEP method and a relativistic pseudopotential with 28 electrons in the core for the central Yb atom. Remarkable agreement of the electronic densities within the YbHal2 fragments with those of the original periodic crystal calculation is demonstrated. The calculated interatomic distances between the central Yb and nearest halide atoms are in pretty good agreement with the experimental data, the deviations are within 0.015 Å for all the studied crystals. Thus, the overall accuracy for the crystal characteristics evaluated using CTEP in the combined periodic-structure and embedded cluster study is comparable with that of Yb-containing molecular calculations.