Okay so idk why you can't send them to BTC-E but that's okay..
SO do this:
Go to Coinbase
go to "Accounts"
--you will see all your wallets (for example: BTC wallet, USD wallet, etc.)
Go to your "LTC wallet" and next to it on the right hand side you should see a small link that says "Rename"
--- under it, you'll see another small link that says "Get Litecoin Address"
Click the link that says "Get Litecoin Address" and a window will pop up with a QR scan code and your generated address under it that you can copy with your mouse or write down if necessary. MAKE SURE THAT IF YOU WRITE IT BY HAND THAT YOU WRITE IT PERFECTLY CORRECT AND CLEAR ON PAPER
Go to your Litecoin QT wallet and send your coins to the address you copied.
Check your Coinbase account. You should see the transaction pending for the most part so give it a few minutes.
Then when you're happy. Donate to me! YAAAAYYYYYY!
Let me know if you get lost or have questions