The idiom no love lost describes a feeling of mutual hostility between two people or groups. For example,
There's no love lost between him and his neighbour.
But is it correct to also use it without the mutual part? For example,
I have no love lost for my neighbour.
meaning that while I feel hostility for my neighbour, he may or may not feel the hostility towards me (or at least, this sentence doesn't make any claim about it).