It is not possible to use Lewis theory to create unambiguous acidity scale. Acid strength can be only determined relative to the selected base (and vice versa), and quite often it happens that depending on the selected base results are opposite (what seems to be a stronger base becomes a weak base after selecting different base as a reference point). In the case of Brønsted-Lowry this is not a problem, even if you move to different solvent relative strengths of acids are identical (or at least their ordering doesn't change - what was stronger is still stronger). In a way that's because proton gives a reference point, but proton presence (or autodissociation of a protic solvent) is one of the theory assumptions.
Try to find Adam Hulanicki's book Reactions of acids and bases in analytical chemistry for some more details (I guess it is n ot a problem to find discussion in other sources, this one I have here so I know it addresses the problem).