“A game dynamic in which the winner is determined solely by chance. This creates a high level of anticipation. The fairness is often suspect, however winners will generally continue to play indefinitely while losers will quickly abandon the game, despite the random nature of the distinction between the two.”
A lottery game mechanic is just as the name suggests. A gambling mechanic where you can get a random item for paying either in game money if it is possible, in like these some Facebook games that have some sort of wheel of fortune, and you get a chance to spin again once you spend some jewels which are only obtainable by paying real life money.
But then there is also the other sort of gambling like the Games Corner from Pokémon games. The main goal was to use up a coin, and just try your luck and try to win a higher amount of coins which you can then later on exchange for rare Pokémon or Items. In the Korean version of a later Pokémon game they did change the slot machines and actually disabled them completely due to the illegal gambling in South Korea. Then in the next release of Pokémon Soul Silver and Heart Gold all of the slot machines were changed to a custom game called Vortolb Switch, apart from the Japanese release as this one had slot machines as well.
An idea I would have in my game with a Lottery system is to allow the player to have a daily chance or rolling random numbers and winning an item of some sort. I could also make something on a line of, you will always get a chance of getting something like a weapon but you have to bet your own weapon in the hope you will get something better.