You should consider using the AJAX API. Once you get the hang of it, it is easier and saves you a lot of headache.
You question specifically: Your Lightbox should produce identifiable markup that you can use to hide the elements you don’t want, much like you’d create a printer friendly page. I don’t specifically know about LightBox, but ThickBox creates several <div>s with the TB_ prefix on the ids, one of which is TB_ajaxContent so…
#TB_ajaxContent .header { display:none }
… will hide the header with class header. Fairly simple, really.
For your other issues, just load the single post page in LightBox and hide the parts you don’t want. Everything should work like normal. You probably don’t even need that callback script, honestly. You can just load the URL of the page you want.