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Since the discovery of magnetic skyrmions in MnSi, systems with topological magnetic textures have been intensively studied due to their possible application in nanoscale memory devices. Even more interesting would be multiferroic skyrmionic systems where the magnetic properties can be, in principle, affected by external electric field through the coupling between the magnetic and ferroelectric order parameters. One of the few known examples are lacunar spinels GaV₄S₈ and GaV₄Se₈ which host Neel-type skyrmions and sizeable ferroelectric polarization. These spinels present a challenge for theory due to the fact that the actual magnetic units are V₄ metal clusters, as suggested by experimental evidence in the literature. In our work, we study the electronic properties of these lacunar spinels using density functional theory and its extensions for correlated systems and calculate the Heisenberg and Dzyaloshinskii-Moriya magnetic interactions, which are necessary ingredients for the skyrmionic behavior, using the RSPt code. The role of magnetization distribution, electronic correlations and ferroelectric polarization is discussed and large-scale simulations are performed to determine the influence of these factors on the magnetic texture.