It doesn’t matter who sent the coins. It only matters who has the private key to the RECEIVING address. The “RECEIVING address” being the address where the coins are right now.
TROM6 sent LTC coins to a BTC address of his own nano ledger s. Since he owns the nano ledger s he had the key to the BTC RECEIVING address and with some “tricks” it was easy to recover the “lost” LTC.
In your case you sent LTC coins from you ledger blue to a BTC address of bittrex. Since bittrex has the key to the BTC RECEIVING address only bittrex can recover these coins. So, you can’t recover it because you don’t have the private key to the BTC address owned by bittrex.
I know you already sent emails to them and they said there’s nothing they can do about it. The fact is, they can, technically at least. But I assume their company policy forbids most of the workers access to any private key. It wouldn’t be safe if everyone there has access to private keys.
So they would need to call one of the bigger guys with higher access rights in order to do something like this. Time is money so they will send you a big invoice and if their invoice is more expensive than the coins you want to recover, there’s no point in doing this.
I think this is the reason why bittrex is not helping you out.