The best site for LTC/BTC trade is
Btc-e.com. I'm surprised to see that no-one mention it yet. I don't really get why people suggest you low volume, untrusted sites. Btc-e is your best bet.
Agreed BTC-e is a great exchange and is the best for LTC volume. Shapeshift.io for small volume works amazingly well. Also people will say that BTCe is some how shady - all exchanges are shady, but I actually trust BTCe over most.
Can you tell me how much the waiting time before the completion of LTC to BTC exchange? or someone will buy LTC for BTC once you posted that your LTC is wts