Basically, yes. You should be able to recover the coins sent "cross-chain", but only if you have the
appropriate private keys.
After all, private keys are really just very large, random numbers... and, as far as I'm aware, both BTC and LTC use the same "range" of private keys. The problems arise because the overlap in Bitcoin and Litecoin addresses was in the "P2SH" addresses if I'm not mistaken... the ones that start with a "3"... whether or not you have the appropriate private key for that type of address is another story!
You can have a play here:
https://www.bitaddress.org/ and here:
https://liteaddress.org/Click the "wallet details" tab, and use this private key: DD4024E95D3171908BF3F20F4CE684F4D09C1D2C08A6047FFC1842CF1E157D81
Bitcoin:
Litecoin:
Same public
keys generated from the same private key, but obviously different "addresses" due to the address encoding using different network bytes etc. Also, the "WIF" format keys will be different as well, but the underlying
hex private key is the same:
Bitcoin:
Litecoin:
(NOTE: how the litecoin code has been copied and says incorrectly that WIF should start with a "5", "L or K"?
)