What is the best depression/pain medicine that goes with lithium?

No such List: There is no such product or list. Psychiatric medications are not prescribed based upon a 'cookbook' of medications. The appropriate medications will vary from human to human and experience to experience.

Bipolar depression: Latuda is approved for use in bipolar depression alone or with lithium or depakote. Other options are seroquel xr or symbyax (fluoxetine and olanzapine) (a combination of Prozac and zyprexa.) Lamictal is often added in but is not actually approved. Symbyax (fluoxetine and olanzapine) causes a lot of weight gain and seroquel xr can be sedating, if it were me, i would opt for Latuda and depakote. Pain med is up to your doc, since you don't specify type.