The microscopic structure of a dilute solution of LiCl in water is determined at different thermodynamic states in both the liquid and glassy phases. This solution exhibits double glass transitions at moderately high pressures and low temperatures, which have been considered as the signature of liquid-liquid immiscibility. Similar phenomena are predicted to be peculiar of liquids with tetrahedral structure, such as water and silicon dioxide, nevertheless a direct structural investigation, based on neutron diffraction has not been performed so far, at least as far as this aqueous solution is concerned.