Single-molecule magnet (SMM) properties of transition-metal complexes coordinated to lacunary polyoxometalates (POM) are studied by means of state of the art ab initio methodology. Three [M(γ-SiW10O36)2] (M = Mn(III), Fe(III), Co(II)) complexes synthesized by Sato et al. (Chem. Commun. 2015, 51, 4081-4084) are analyzed in detail. SMM properties for the Co(II) and Mn(III) systems can be rationalized due to the presence of low-energy excitations in the case of Co(II), which are much higher in energy in the case of Mn(III). The magnetic behavior of both cases is consistent with simple d-orbital splitting considerations. The case of the Fe(III) complex is special, as it presents a sizable demagnetization barrier for a high-spin d(5) configuration, which should be magnetically isotropic. We conclude that a plausible explanation for this behavior is related to the presence of low-lying quartet and doublet states from the iron(III) center. This scenario is supported by ab initio ligand field analysis based on complete active space self-consistent field results, which picture a d-orbital splitting that resembles more a square-planar geometry than an octahedral one, stabilizing lower multiplicity states. This coordination environment is sustained by the rigidity of the POM ligand, which imposes a longer axial bond distance to the inner oxygen atom in comparison to the more external, equatorial donor atoms.