Simulations of Density Functional Theory-based ab initio molecular dynamics (AIMD) have been performed for a series of aqueous lithium bis(trifluoromethylsulfonyl)imide (LiTFSI) solutions with concentrations ranging from salt-in-water to water-in-salt systems. Analysis of the structure of electrolytes has revealed a preference of Li+ cations to interact with water molecules. In concentrated LiTFSI solutions, water molecules form small associates. The total number of hydrogen bonds (HBs) in the system decreases with salt concentrations, with bonds to water acceptors being only partially replaced by interactions with TFSI anions. Infrared (IR) spectra in the region of the O-H stretching frequency calculated from AIMD trajectories are in good agreement with experimental data. Statistics of oscillations of individual O-H bonds have shown correlations between vibrational frequencies and the structure of HBs formed by water. The changes in the IR spectrum have been related to the varying contributions of different local environments of the water molecules. The abundances of the three spectral components calculated from the simulations agree well with the decomposition of the experimental IR spectra reported in the literature.