When you instruct your litecoin-core to abandon an unconfirmed transaction, your litecoins “get back” to your balance, so you can spend them.
For your transaction to be confirmed, it has to reach all the nodes on the network and then, it needs to be included in a new block by a minner. Broadcasting the transaction is the process your node uses to let all the nodes it knows about your new transaction, this way it will eventually get to a miner who will include it on a new block.
However, by some reason, the network seems to not know about your transaction, and thus it is unlikely to ever get confirmed.
For your safety, you should either:
- Re-broadcast the transaction to get it confirmed by a miner,
Or abandon it and make a new transaction
So it’s up to you, if you prefer your current tx to get confirmed, or if you prefer those litecoins to “get back” to your balance and spend them in a different way.