I found what I think is a better solution than those listed above using Lightbox 2 version 2.6. On line 252 of lightbox.js (unminified), you'll see this line which adds the caption:
this.$lightbox.find('.lb-caption').html(this.album[this.currentImageIndex].title).fadeIn('fast');
Once the caption is added, you can register the click event and force the browser to follow any link in the caption by adding onto the chain like this:
this.$lightbox.find('.lb-caption').html(this.album[this.currentImageIndex].title).fadeIn('fast').find('a').on('click', function() { location.href = $(this).attr('href') });
I've initiated a pull request with this change so you can follow the status and any further discussions there.