Infrared (IR) spectra of solutions of the lithium salt LiBF4 in the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate (EmimBF4) and in the organic solvent propylene carbonate (PC) are studied via infrared spectroscopy and ab initio molecular dynamics (AIMD) simulations. The measurements show that the major effects of LiBF4 in both solutions, compared to their neat counterparts, are the appearance of a new broad band in the 300-450 cm-1 frequency region and a broadening of the IR structure in the 900-1200 cm-1 region with the development of a new peak at 980 cm-1. Computational analysis indicates that hindered translational motions of Li+ in its solvation cage are mainly responsible for the former, while the latter is due to Li+-induced structural changes and accompanying vibrational frequency shifts of constituent ions and molecules of the solutions. In addition, molecular motions in these and lower-frequency regions are generally correlated, disclosing the collective nature of the vibrational dynamics, which involve multiple ions/molecules. Herein, a detailed analysis of these features via AIMD simulations of the spectrum and its components arising from auto- and cross-correlations of motions of constituent molecular species, combined with generalized normal modes of the solutions and normal modes of small Li+-containing clusters, is presented. Other minor spectral changes caused by the lithium salt as well as the interaction-induced effect on IR spectra are also discussed.