First, welcome to Psych Central.
Second, if it were me, I would not quit - it only makes things worse to be unmedicated and unsupervised. Is it possible to change doctors? It sounds like that would be a better option, especially if you are suicidal and getting inappropriate meds.

If it is not possible to change docs, then you have to take responsibility for making sure your docs don't prescribe too much - remind the md that 56 pills is too much for you, as you have the problem with being suicidal, or give the pills to someone you trust, who will only give you a non lethal amount at a time. Remind the pdoc that she said she wouldn't give you lithium, and flat out tell her she needs to find another option, if you can't take the lamotrigine. There are a lot of mood stabilizers on the market, not just those two. For example, I take trileptal. Tegretol is another, older, drug. I'm sure others can tell you some of the more recent mood stabilizers. A little trial and error, and you should be able to come up with one you like.

I know the pdocs like to be in control, so don't be aggressive with her, just assertive. And remember that you have to keep track of things if your docs aren't. But first, I'd just try changing docs.