So, basically, you are buying a car from someone who needed to finance it, then wants to sell it before the term of finance is up. To me, you are dealing with someone who isn't the best planner or the most financially responsible. I would contact the lien holder directly, pay off that amount directly, then pay the difference to the seller.
Precision tool: 2011 BMW ///M3
Sledgehammer: 2014 Audi S6