How can I add a class to link around image field
From the way lightbox does it (line 145), i would think there is not much you can do to alter the link, since it is "hardwired" there.
What you could do (and is surprisingly easy :) is to implement your own handler that would extend the lightbox one and allow you to specify the css class (or submit a patch that would do it in their code).

You might as well specify the class on the parent div (in views "Styles settings" for the field, "Customize field HTML" and "Create a CSS class". And then just sligthly change your selector.