Honestly, there is nothing that can be done. With a 2-of-2, you absolutely need 2 signatures to be able to send funds. If all that GreenAddress provided is an nLockTime partially signed transaction, that isn't going to be of use to you as it will have been signed for BTC (sending to a BTC address) and not for LTC.
While the addresses can be compatible, I don't think the transactions are (ie. You can't create a BTC transaction and transmit it in the LTC network).
"Cross-chain" transactions involving MultiSig can be extremely difficult to recover from unless you have all the keys