If lime does help gout symptoms it is more a matter of the antioxidants it contains than the pH. For these to have any effect, the limes need to be fresh and not pasteurized, weeks old juice in a bottle and, as is generally the case, made from concentrate and diluted with town water.
I have found Kakadu Juice taken at twice the recommended level for general health improvement, to totally stop any symptoms of gout for over 2 and a half years now. I also still enjoy meats, bread (daily), beer (sometimes quite a few), prawns and all the things which I couldn't eat previously.
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