Classical molecular dynamics (MD) simulations and quantum chemical density functional theory (DFT) calculations have been employed in the present study to investigate the solvation of lithium cations in pure organic carbonate solvents (ethylene carbonate (EC), propylene carbonate (PC), and dimethyl carbonate (DMC)) and their binary (ECDMC, 1:1 molar composition) and ternary (EC-DMC-PC, 1:1:3 molar composition) mixtures. The results obtained by both methods indicate that the formation of complexes with four solvent molecules around Li$^+$, exhibiting a strong local tetrahedral order, is the most favorable. However, the molecular dynamics simulations have revealed the existence of significant structural heterogeneities, extending up to a length scale which is more than five times the size of the first coordination shell radius. Due to these significant structural fluctuations in the bulk liquid phases, the use of larger size clusters in DFT calculations has been suggested. Contrary to the findings of the DFT calculations on small isolated clusters, the MD simulations have predicted a preference of Li$^+$ to interact with DMC molecules within its first solvation shell and not with the highly polar EC and PC ones, in the binary and ternary mixtures. This behavior has been attributed to the local tetrahedral packing of the solvent molecules in the first solvation shell of Li$^+$, which causes a cancellation of the individual molecular dipole vectors, and this effect seems to be more important in the cases where molecules of the same type are present. Due to these cancellation effects, the total dipole in the first solvation shell of Li$^+$ increases when the local mole fraction of DMC is high.