this is a good lesson to double and even tripple check where are you sending your coins to
lucky you you had the keys to the address
I had a similar situation a couple of years ago,lost 4.2 litecoins this way,sent them to a bitcoin address at an exchange
evidently,support could not retrieve the coins due to them having no access to the client's private keys
so I had to give up trying to escalate it,besides the sum was really low at that time
I sent 10 Ltc to a site that generates me a deposit for a coin exchange site.
maybe the exchange took your ltc?
they surely did,I could not recover them because support refused to get access to their wallet's private keys

maybe you didn't get what I posted-it was LTC sent to a BTC addy,thus it was a mistake on my part