There hasn't been anywhere near as much as research into this as there should be. This is a bummer, as many people are interested in taking psychedelics to alleviate mental health issues which they currently take psychiatric medications for.

The task of studying contraindications between psychedelics and mental health conditions is mind-bogglingly complex given the number of combinations possible, and we've yet to find a truly definitive guide to what we know thus far.

Here's one table we've found about combining antidepressants with psychedelics, though it doesn't include lithium specifically.

As to what's happening to your brain on lithium and psychedelics, it comes down to the specific psychedelic and your specific brain, which even a trained expert would not be able to fully determine or predict.

That said, if you have had negative experiences taking psychedelics on lithium, it's probably a good idea to avoid doing so in the future: your brain could be trying to send you a message, and it's a good idea to listen when that happens.