As I reconstruct the statute before the 1994 amendment, it read as follows:
Whoever brings into the United States for the purpose of disposing of the same, or knowingly deposits with any express company or other common carrier for carriage, or carries in interstate or foreign commerce any paper, certificate, or instrument purporting to be or to represent a ticket, chance, share, or interest in or dependent upon the event of a lottery, gift enterprise, or similar scheme, offering prizes dependent in whole or in part upon lot or chance, or any advertisement of, or list of the prizes drawn or awarded by means of, any such lottery, gift enterprise, or similar scheme; or knowingly takes or receives any such paper, certificate, instrument, advertisement, or list so brought, deposited, or transported, shall be fined not more than $1,000 or imprisoned not more than two years, or both.
This was a very old statute, dating back to 1909. I think given its construction it refers to carrying or transmitting in interstate commerce the actual lottery ticket or other paper that was issued to participate in the lottery. While there might be a way to construe it to extend to what you described, criminal statutes cannot be vague in order to be enforceable. It must be clear what the statute prohibits, and in my view it isnít so clear under the pre-amendment version of this Code provision. So, it might have been subject to attack on the grounds of being vague if the feds tried to prosecute it. That may be why Congress decided to make it clear in the amendment that this kind of service is illegal, too.