It may be the Xanax that is decreasing your anxiety, Lithium is really not an anti-anxiety med, but can help tremendously in the long run, and yes, your pdoc is right about once you achieve your therapeutic dose of Lithium,he or she will most likely be able to wean you off the other meds, just keeping an anti-anxiety med to use only as needed.
When I was established at therapeutic dose for my mood stabilizer, I no longer needed any AD's and have Ativan that I use only when I am feeling a lot of anxiety brought on by life situations such as being a caregiver as well as this pre-menopausal hormone shifting.
The main med. for Bipolar should start with a mood stabilizer, then if needed, other meds can follow.
So often Bipolar goes undiagnosed,being mistaken for depression, which the patient gets only partial treament or wrong treatment.
You'll be surprised how the main med can help other symptoms, as well as anxiety.
Hang in there, good things will happen, sometimes it takes awhile, but is worth being patient with new treatment plan(s).
Glad you have come to our forum(s) at PC.
Take care,
DE