Where do you get your BTC address from? It might be possible that you copied your address wrongly, just a possibility, or your address requires some deposit fee and it may have caused some trouble when the BTC was sent.
Do you mind telling more details about your wallet address? (Exchange site, online wallet... etc)
of course
i'm using block.io for both litecoin and bitcoin
check :https://block.io/
block.io is really secure and i had no issue with it in the past !
i did many exchanges from litecoin to bitcoin using other exchanges with no issue !
you can check my address on the order
https://shapeshift.io/#/status/4d4c2e03-87c7-461a-b0e8-ea1b5cdd1c47it's :3JM51zK1QM9sqHkD1jysBmdAamoDPXJNLr
Now i sent to myself 0.1 btc and it worked
check :
https://blockchain.info/address/3JM51zK1QM9sqHkD1jysBmdAamoDPXJNLrso it shouldn't be an issue for them to exchange 44ltc and send them!!