Online, mobile or a hardware wallet, all types are available for Litecoin, for storing and processing the coins. There are two official desktop wallets and an iOS app with Android to become available soon.
Litecoin Core - the Official Litecoin Wallet (Desktop)
This is the official wallet for Litecoin. It’s a desktop wallet available for Windows, Mac and Linux, and no registration or personal information is required to use it. It is also free to use.
It synchronizes with the entire blockchain, which can take a few days. Using this wallet helps secure the entire network.
Electrum LTC (Desktop)
A fork of the Bitcoin wallet Electrum specifically created for Litecoin. It is available for Mac, Windows, and Linux.
The advantage of Electrum LTC is its fast synchronization.
Trezor (Hardware Wallet)
Trezor was first created to be used with Bitcoin, but it can be used for Litecoins as well.
Ledger Nano S (Hardware Wallet)
Another hardware wallet where Litecoin is stored offline directly on the device. Whenever you want to spend your Litecoins, Ledger Nano S signs it using the private key stored on the device.
Jaxx (Mobile Wallet)
The multi-asset wallet by the Canadian company Decentral, supports multiple cryptocurrencies and LTC is one of them. Jaxx is elegantly designed and features robust security. Private keys never leave the device.
Jaxx wallet runs on desktops on Windows, Mac OS, Linux or as an extension in Chrome and Firefox, it also has a mobile app for both Apple and Android.
LoafWallet (Mobile Wallet iOS only)
A mobile wallet that’s easy and safe to use. Developed originally by Charlie Lee, now maintained by the Litecoin Foundation. An Android version is on the 2017 roadmap.