How to balance out sourness of lemon juice, specifically in a mayonnaise?
To balance acidity, add sugar.  It's how most mayonnaise manages to be acidic enough to prevent bacteria growth (pH 4.6 or lower), while still having a balanced and edible flavor.  

You might get an edible result with honey, but sugar is more of a neutral flavor, so I would use that first.  Using a jigger of Dijon mustard is not beyond the pale, as well... might help hide the acid, to a lesser extent.