We report a study on the hydrogen-bond network of water in aqueous LiCl solutions using X-ray Raman scattering (XRS) spectroscopy. A wide concentration range of 0-17 mol/kg was covered. We find that the XRS spectral features change systematically at low concentrations and saturate at 11 mol/kg. This behavior suggests a gradual destruction in the hydrogen-bond network until the saturation concentration. The surprisingly large concentration required for the saturation supports an interpretation in which the ions affect the structure of water only within their first hydration shell. The study is complemented by density-functional-theory calculations and molecular dynamics simulations.