This is not a bad idea at all but you must keep some things clearly in your mind
Now my question for Cryptocurrencies dev :
What do you think about offer to your users, a way to win some giveaway/bounty of your Cryptocurrency, by playing with a label of game/app?
The games should be not for only One cryptocurrency, the player could win some generic coins, and exchange them with Your Coins, based on a change rate that you could set up.
There are very few people that are faithful to one coin or another, so nobody has "his users". People use a coin, whether buying it, mining it, exchanging or staking it - but they are not going to hold it like forever, they spend some time with it to get
profit.
To resume: Your fan could be able to play to some "CryptoGames" (Android or iOS) to win "CryptoCoin" on their accounts.
Then, the player could exchange his CryptoCoins to you Coins, with your exchange rate. We could setup a maximum amount/player, and a lot of other things.
Again, there are no fans.
People use cryptocurrency as money, they exchange it, hold it, stake it or whatever, but they are not playing with it, so you can't really refer to them as "fans", like they're playing Pro Evolution Soccer. And there is no way to setup a price for a coin, the price is set by the market itself and changes every second with huge ups and downs.
What you can do is offer coin A or coin B from your app, send it to the user's wallet and he will decide to do whatever he wants with it. Maybe you could have a list of coins and, whoever will play this game, choose the coin he prefers. This way you will attract newcomers and those who are happy to earn some coins for free, like from faucets etc.
As for Litedoge, since you asked me in pm, I will forward your request to the right people and we can probably work something out. Litedoge is a community coin, there is a large number of people deciding about its future, so I cannot really give you an answer all by myself.