In sword and Shield, it will check a number and the Trainer ID of a Pokémon in your box I think, so If I get the number using the Rotom lottery, then close the game if I make a Pokémon on the 3DS and send it up with the same number as the lottery number then will I be able to get the top reward?
Nope. You have to save the game to draw a ticket, so there's no way to try again after you've received a number.