To characterize the structural relaxation of an aqueous solution of LiCl, frequency-dependent shear rheological experiments are carried out near its glass transition. Analyzed within the fluidity representation, the generic spectral shape that was previously found for a range of different kinds of glass formers is confirmed for the currently studied hydrogen-bonded fluid as well. Furthermore, the validity of the rheological equivalent of the Barton-Nakajima-Namikawa relation is demonstrated for the aqueous LiCl solution. Its mechanical response is compared with that obtained using dielectric spectroscopy, a technique which is sensitive to both the reorientational dynamics of the water molecules and the translational dynamics of the ionic species. The extent to which these electrical polarization processes are coupled to those governing the viscoelastic response is discussed, also in comparison with the behavior of other ion conducting liquids.