From the documentation files: http://lokeshdhakar.com/projects/lightbox2/
You do not need to initiate anything, any image link with the data-lightbox
attribute like this:
<a href="img/image-1.jpg" data-lightbox="image-1" data-title="My caption">Image #1</a>
will work automagically even if loaded by AJAX as soon as you add it to your DOM.
EDIT: After having taken a look at the lightbox script, you may have to change as well the line #51:
$('body').on('click', 'a[rel^=lightbox], area[rel^=lightbox], a[data-lightbox], area[data-lightbox]', function(event) {
into this:
$('body').live('click', 'a[rel^=lightbox], area[rel^=lightbox], a[data-lightbox], area[data-lightbox]', function(event) {