Is there a way to retrieve lost Litecoin one year ago, I transferred few litecoins to btc-e, which after few days were shut down, from my wallet.

At that time, my wallet was not fully synced with the network. 

In my wallet I can still see that the transaction is unconfirmed (0 of 6 confirmations).

Is there any way to retrieve the litecoins?
Was your wallet not fully synced before the transaction? And still is in the same block as then?

If the answer to both of them are yes, then you may have a chance.

What you have to do is:

Verify the transaction in a Litecoin explorer

If you don't know the transaction, just input your address in the explorer and check it's balance.

If it still says you have balance, I recommend you to import your private key to some other lite client and use it however you want.

To retrieve private key from Litecoin-qt wallet, I would suggest this answer.