There is no way this could happen, transaction would result in error.
If was from some service then contact their support, if from your wallet then reset the chain or export the key to other wallet because the transaction never happened
~considering the destination address will be wrong. ~
no it won't if he used a multisignature address!
Litecoin used to have the same version field (which resulted in multi signature addresses start with 3) as bitcoin so it is possible to send LTC to BTC address and vice versa and don't get any errors. because it is a valid address.
they changed this to "M" recently though. but the old addresses will remain valid forever!
since these two use the same method of creating an address they both have the same private keys in code level so you have a hope of recovering it.