Here is the email response I received from their support team:
Dear Tammy
Thank you for contacting theLotter.com - the Global Lottery Service.
As was explained to us by our Visa credit card processing company and as your credit card company is probably reluctant to admit, some Visa issuers, including yours, refuse transactions from sites classified as 'gaming'.
We do apologize for the inconvenience.
When playing on our site we suggest you use a different type of credit card, i.e. MasterCard, American Express or Diners Club.
To register a different credit card in your account, please select the Add Payment option at your My Details in 'My Home' section.
Please mark the new payment method as your default by signing 'V' in the box next to it.
Dont forget to press the Save Changes button, otherwise your changes will not be updated in the system.
You can also pay for participating in your favorite lotteries with a VIRTUAL MasterCard through Wirecard which is a member of the Association of German Banks.
Opening your Wirecard account and having your virtual MasterCard issued to you is completely FREE of charge.
You can deposit funds to your Wirecard account via bank wire, Direct Debit (ACH), Credit Card or Cash deposit.
We hope you find this information useful and satisfactory.
Customer Service Team
theLotter.com