There are many exchanges out there which enables a person to trade crypto to crypto such as yobit, hitbtc, livecoin, cryptopia etc... All of these exchanges accepts BTC deposits and withdrawals without any type of ID verification. I would suggest yobit as it is smooth and has less fees when compared to other exchanges. You can also try livecoin and cryptopia for the exchanging your BTC to LTC.
I wouldn't recommend to try Yobit due to many problems with this trading platform.
Actually, all the verification steps are important thing, at least verify your email, but for most exchange you have to provide an ID to be verified depends on which exchange and where you live, local exchange in your country is always the best option to deposit btc and withdraw ltc.