How much filler is required for just the vermillion border of the lips?

one 1 cc syringe is enough. Most important factor is experience and aesthetic judgement and knowledge and taste of the injector and not the filler!  

This all depends on the lip itself.  This may take 0.1cc to a full syringe.  I think you need to post photos or do see a facial contouring expert for an evaluation.  Best, Dr. Emer.

Upper lips usually take 1 cc which is 1 syringe which does great and lasts about 6 months for restylane, belotero, juvaderm.

In my practice, I rarely inject more than 1 syringe (1 ml) into the lips.  Having said that, the amount required for each individual varies significantly.  It would be best to do a consultation with an expert and decide from there.  I've included a web page for reference.  Good luck. 

If you only want to establish a "new lipstick line" and improve the philtral columns and cupids bow, typically less than one syringe of hyaluronic acid is needed - for example Restylane or Juvederm.  Most fillers come in 1 ml syringes, and the average for these areas in our practice is about 0.6 ml.  The remainder of the filler can be used to augment the lips or fill lines and creases around the mouth.  You can use more, but often this leads to a more "stylized" and less natural appearance.

Most likely 1 syringe will be enough for your lips.   That should give you a nice lip line with a great philtral column and cupids bow!