Organic carbonates and their mixtures are frequently used in electrolyte solutions in lithium-ion batteries. Rationalization and tuning of the related Li+ solvation processes are rooted in the proper identification of the representative low-energy spatial structures of the microsolvated Li+(S)n clusters. In this study, we introduce an automatically generated database of conformational energies (CEs), LICARBCONF806, comprising 806 diverse conformers of Li+ clusters with 7 common organic carbonates. A number of standard and composite density functional theory (DFT) approaches and fast semi-empirical methods are examined to reproduce the reference CEs obtained at the RI-SCS-MP2/CBS level of theory. A hybrid PBE0-D4 functional paired with the def2-QZVP basis set is the most robust in reproducing the reference values while composite B97-3c demonstrates the best cost-benefit ratio. Contemporary tight-binding semi-empirical methods GFNn-xTB can be used for the filtering of high-energy structures, but their performance worsens significantly when the limited number of low-energy (CE < 3 kcal mol-1) conformers are to be sorted. Thermal corrections used to convert electronic energies to respective Gibbs free energies and especially corrections imposed by a continuum solvation model can significantly influence both the conformer ranking and the width of the CE distribution. These should be appropriately taken into account to identify lowest energy conformers in solution and at non-zero temperatures. The almost black-box conformation generation workflow used in this work successfully predicts representitative low-energy four-coordinated conformers of Li+ clusters with cyclic carbonates and unravels the complex conformational nature of the clusters with flexible linear carbonates.