do not use online wallets and certainly do not use an exchange site for storing any coins not only litecoin because of the risks these methods have.
Whilst using online wallets are generally not recommended for long term storage of Litecoin, it would be preferable for people to use
litevault.net. LiteVault was built by a well known LTC enthusiast, and coblee has personally vouched for the usage of the site.
LiteVault doesn't have access to any of your coins, and can only see an AES cipher of your private key. When you log in, your password deciphers the private key. Everything else is done within your browser (through bitcoin-js).
I am not arguing about the safety of online wallets like the one you suggest and the full explanation of it by someguy123 in two comments below yours.
all I am saying is that nothing will ever beat the cold storage. and this is something you can do with an offline computer, a live Linux, to either generate a private key and print it on a piece of paper or install a wallet like Electrum-ltc which also lets you have a watch-only-wallet on your online pc without the private keys to watch and spend .