The more Pokemon you have from other trainers, the more chances you have to win the lottery. Since each trainer's Pokemon have a unique ID number, trading with as many other trainers as possible greatly ups your odds of winning.
The only way to win the lottery is with an exact number match. If you have no Pokemon from other trainers, you should trade before trying to win any of the lottery's top prizes; otherwise, it could be a long time before you actually win.
Each day (or each week in Generation II), a random ID number is generated; if the player has a Pokémon with the same or a similar ID, they will receive a prize. In order for a Pokémon's ID to be eligible for an award, one or more consecutive corresponding digits of the Pokémon's ID and the random ID must be the same, starting from the rightmost digit. For example, if the current lottery number is 12345, a Pokémon with the ID 12340 will not win, and one with the ID 12305 will win for matching only the last digit (except in Generations II and III, which do not give rewards for matching only one digit).
Getting a prize in Emerald depends on how many digits of that day's ID number are matching. Simply trading does up your chances, but I don't believe it matters what language the traded Pokemon are. You can only get a Master Ball from 5 matching digits, so it is pretty rare.