No, unfortunately it is not allowed to do that on the forum. You can do giveaways off-site (for example, google form) and post a link in this thread, but you can't give people any incentive for replying to your thread.
Alternatively, instead of giving away Litecoin, Mitch212 could use an instant exchanger (such as FixedFloat) and convert it to Bitcoin. That way, he's allows to make an on-forum giveaway in Games and Rounds.While I understand that the rules are there to avoid mindless spam, I also feel for users like OP and maybe we can do something about it.
I tried: Suggestion: allow on-forum altcoin giveaways for established altcoins. It didn't happen.you can't give people any incentive for replying to your thread.
Unless you ask them to post the same "proof of authentication" BS in dozens of threads, then it's totally fine 
I feel that there should be a giveaway subforum under Bounties.
I get why on-forum altcoin giveaways were banned: it lead to huge spam. But considering the millions upon millions of useless bounty posts, I don't think giving away some actual value in any altcoin would be worse than that.