in a former version of lightbox support, they gave this answer to "Can I insert links in the caption?"
Yes, but you need to convert quotes and greater and less than symbols into their html entity equivalents. For example:
<a href="images/image-4.jpg" rel="lightbox" title="<a href="link.html">my link</a>">Image</a>
I think that this will work adapted to your pdf links as well.
Otherwise you could ask your question in lightbox' forum: http://lokeshdhakar.com/forums/. One question I found there which is similar to your problem, I think:
... and if contrary to my expectations you will not be successful in your efforts I'll join DG/L's proposal.
hans-g is correct. You have to convert the double quotation marks and greater than/less than symbols to their entities. Here's a reference to HTML Entities: