Yes, you can—you’ll just need to check out with two items in your cart.
First, customize your postcard (with or without a mailing list) and add it to your cart.
From the cart, click the Copy icon, then select Customize on the duplicated item. You’ll be taken back to the beginning of the customization process.
From there, you can update the mailing list selection (add or remove a list) and add the second version to your cart.