We have characterized the structure and picosecond dynamics of the hydrogen bond network of solvated LiI by means of first-principles molecular dynamics simulations at ambient temperature. Our calculations reveal the qualitative differences of the network between low (1 M) and high (9 M) salt concentrations. In particular, we find the presence of fused Li+ solvation shells at 9 M, meaning that a single water molecule is coordinated to two different Li+ ions. This results in the formation of (Li+center dot H2O)(n) chains, dominating over conventional ion pairing. We report experimental and simulated NMR chemical shifts, which indicate a weakening of the hydrogen bond network, mainly within the first solvation shell of the I- ions. In line with this finding, the local dynamics of this network reveal a competition between the chaotropic effects of I+ and the kosmotropic properties of Li+ ions at an intermediate range. We find that the chaotropic effect of I- reaches across several H-bonds into the solution, whereas the kosmotropic effect of Li+ is more short ranged.