I'm not an expert, but my understanding is that Lithium is used for bipolar.
It is possible that she has both bipolar and BPD. In which case, the Lithium could be effective for the bipolar.
It is possible she has been miss-diagnosed with bipolar instead of BPD. In which case, it is unclear whether Lithium will help. Maybe unlikely more than unclear.
You might want to read this:
What is the relationship between BPD and bipolar disorder?