the good thing about Litecoin is that it is old and a copy of bitcoin and also has a good development team. all these means you have lots of options, very similar to bitcoin options for storing long term. so your answer is the same as bitcoin for long term holding.
1. hardware wallets. i believe Trezor and possibly others support LTC.
#this is a costly method but easy and secure.
2. paper wallets. there is a nice fork of bitaddress.org called liteaddress.org which you can use to generate a secure paper wallet offline
https://github.com/litecoin-project/liteaddress.org#this is free but harder to use, you need to sweep it later when you want to spend and create a new one.
3. SPV wallet called Electrum-ltc which is similar to Electrum for bitcoin (a fork of it) which is light an small.
https://electrum-ltc.org/ you can use the same cold storage guide from Electrum for this also:
http://docs.electrum.org/en/latest/coldstorage.html#this is more flexible, but can be a bit complicated to use as cold storage. but very easy to use as your hot desktop wallet.
4. obviously the official wallet called litecoin core which is a full node like bitcoin core
https://litecoin.org/#download#this is hard to sync since the blockchain size is big.
