A systematic study of the properties of high-density amorphous ice (HDA) in the presence of increasing amounts of salt is missing, especially because it is challenging to avoid ice crystallization upon cooling the pressurized liquid. In order to be able to study HDA also in the presence of small amounts of salt, we have investigated the transformation behaviour of quenched aqueous LiCl solutions (mole fraction x < 0.25) upon pressurization in a piston-cylinder setup at 77 K. The sample properties were characterized by in situ dilatometry under high pressure conditions and after recovery by ex situ powder X-ray diffraction (XRD) and differential scanning calorimetry (DSC) at ambient pressure. Two regimes can be identified, with a rather sharp switch at about x = 0.12. At x < 0.12 the samples show the phenomenology also known for pure water samples. They are composed mainly of hexagonal ice (I-h) and experience pressure-induced amorphization to HDA at P > 1 GPa. The observed densification is consistent with the idea that a freeze concentrated LiCl solution of x = 0.14 (R = 6) segregates, which transforms to the glassy state upon cooling, and that the densification is only due to the I-h -> HDA transition. Also the XRD patterns and DSC scans are almost unaffected by the presence of the segregated glassy LiCl solution. Upon heating at ambient pressure HDA experiences the polyamorphic transition to low-density amorphous ice (LDA) at similar to 120 K, even at x similar to 0.10. Based on the latent heat evolved in the transition we suggest that almost all water in the sample transforms to an LDA-like state, even the water in the vicinity of the ions. The glassy LiCl solution acts as a spectator that does not shift the transformation temperature significantly and experiences a glass-to-liquid transition at similar to 140 K prior to the crystallization to cubic ice. By contrast, at x > 0.12 the phenomenology completely changes and is now dominated by the salt. Hexagonal ice no longer forms upon quenching the LiCl solution, but instead LDA forms. A broad pressure-induced transformation at >0.6 GPa can be attributed to the densification of LDA, the glassy LiCl solution and/or glassy hydrates.