Like the previous post, I've also gone through various types of semi-formal interviews with faculty at my undergrad school for getting my LORs.
If this professor is potentially one of your "strong" LOR writers, then I would take it seriously enough to give a good "presentation" of yourself.
Even if you'd might look and feel weird about getting dressed up to show up at his/her office on campus (when it's half empty by now since its summer break), I believe that impressions do play apart.
Whether you like it or not, the way you present yourself can help (but not hurt) your efforts to convince your professor that you are VERY SERIOUS about getting into dental school.
I also think that your appointment should be taken as a practice interview.
I've managed to practice my interviewing skills by taking all my appointments somewhat seriously... I can honestly say that it has eased my nervousness when I have to "present" myself.
Good Luck to you!!!