One of the bank's vendors has a sweepstakes and is the sponsor. The bank wants to put an ad on their website for the sweepstakes which would be for an increase in transactions and will be entered for a chance to win. The ad has the "No purchase necessary...", timeline of the sweepstakes, age, etc but it also states that it is open to registered accountholders in good standing at a participating FI. Now, to me it seems like it is not open to the public and therefore could be considered a lottery vs. a sweepstakes. What if the ad is only on a page that accountholders see, would this then be considered a sweepstakes?

Something that is not open to the public is a lottery, as consideration (being an accountholder), would be required to participate.