Hindsight is perfect
We have the benefit of hindsight, and obviously Farewell My Concubine is a huge success.
English translations are meant for foreigners, therefore it should be easy for them to pronounce and remember. At the same time the translation should convey the original meaning. I think concubine is better than lover because the former conjures up an image of ancient time with rich and powerful men, while the latter is applicable to men today of all classes.
Also, "parted with lover" is not appropriate. It can mean he dumped her, she jilted him, he broke up with her, etc.