We don't count hacks made by pirates that aren't offical games as Mario games. In the case of Mario Lottery I don't know, though. Probably it's just another crack but maybe...
First of all there are no title screen or any copyright anywhere to be seen. The word Nintendo is nowhere to be seen.
The game is basically a slot machine with a Mario like character in the middle with an "F" on his cap.
You place bets on deifferent incons around the screen and then they circulate and whne they stop you get points based on how you betted.
The big qeustion is, if it is just a weird NES game that was released by Nintendo in Japan, _why_ does the Mario character have an "F" on his cap?