12 USC Ch2, Sec. 25a - "The term "lottery" includes any arrangement whereby three or more persons (the "participants") advance money or credit to another in exchange for the possibility or expectation that one or more but not all of the participants (the "winners") will receive by reason of their advances more than the amounts they have advanced, the identity of the winners being determined by any means which includes --
(A) a random selection;..."
Interpretations in the past have held that the fees a customer pays the bank fits the "advance money to another" requirement and they hope to win more than they pay. This could classify your program as a lottery. For this reason these programs are generally open to the public. That is what gets them away from being a lottery.
I can't say that your program is or isn't. While you might assume there is a bright line test here, this isn't always the case. How conservative are you, what risks would you assume making your own interpretation, and will state laws come into play? You must answer these questions, or simply contact counsel.
Opinions stated are not necessarily that of my employer.