Q:

Can I find out on which website I got my Litoshi address?

I can't remember where I got my Litoshi address. Is there a way I can find it because boxlit transferred my litoshis already?
I saw the transaction through block.io. I don't think I got it there (block.io). I did not write it down because I always save my username and password in websites I register and sign, but the problem is, I can't remember what website.

A:

Look at a list of Litecoin web wallets to see if any one them sound familiar to you:

LiteVault - Online Litecoin Wallet; private keys encrypted locally
Hive Web Wallet - Online BTC/LTC wallet; private keys encrypted locally
Liteaddress.org - Litecoin address generation tools (BIP38)
Reddit LiteTip Bot - Give and receive Litecoin tips from reddit users
Coinkite - Coinkite is a web wallet with merchant services, Point-of-Sale 
terminals and debit cards. 
CoinWallet.co - Online wallet
Harborly - Online wallet that can be linked with any US bank account
HolyTransaction - Online wallet, multi-currency support
Celery - Online wallet
Cryptonator - Multi coin wallet

https://litecoin.info/Category:Services#Wallet_services
If you are able to locate your account, please send your LTC to an offline wallet with a strong password that you do not use on multiple sites. 
Web wallets are not the most secure and your practice of reusing passwords on many websites is a horrible security practice.

