There is a big issue with invoices generated in some circumstances, for example on anonymous orders. Sometimes the line items are not included in this view and you just see the message "No line items found"!
But this is not a commerce_billy_mail.module or commerce_billy.module bug. It's a problem within the entity permission concept, that leads to this.
There are already some discussions about that, which I'd like to mention:
The solution (at least for my case) was mentioned in this issues: Disabling SQL Query Rewriting for the "Line Items" view. For example look here: https://drupal.org/comment/6063012#comment-6063012
The main problem is being discussed here and I think it's related:
Hier ist der zugehörige Issue von mir auf Drupal.org zu finden: https://drupal.org/node/2201921