came across this thread and thought i'd share. i went through the exact same thing on the same medication combination. everyone's different of course, and our bodies are very individualistic about how they respond to things, but...
i was also on wellbutrin and lithium at the same time for about 3 months. the dizziness and vision issues were terrible. it was giving me mega-headaches, and i couldn't drive or read or look at my computer monitor. at first, my pdoc recommended i take fish oil daily for the eye problems, and it actually helped tremendously. i still take it. his thinking was that the meds were drying my eyes out severely, even though i was using eye drops, and making things worse. however, the dizziness (and some other symptoms) persisted. my lithium level at the time was below therapeutic level (i was at 450 mg a day), and we eventually figured out it was the wellbutrin. i stopped the wellbutrin, and the negative symptoms all vanished (well, besides the depression). later, my lithium levels were increased and i am on a different antidepressant, and doing well.
so in my experience, the wellbutrin was what caused the symptoms you are describing (although i'm sure accidentally doubling your lithium was very pertinent >.<).
hope you've figured it out, and if not, i hope this helps!