Welcome to HW! Hope being here helps you.
Unfortunately weight gain is one of the more common lithium side effects -- and in fact many bipolar meds, although this seems to happen for different reasons. I don't have any personal experience of this, but I did find what looks to be a helpful web article with useful links: http://www.psycheducation.org/hormones/Insulin/weightgain.htm
Is this something you've discussed with your psychiatrist and/or psychologist? That does sound like a big leap in weight over a relatively short period. It's just possible that Depakote would be better for you -- though there are different types of bp that respond better to Dep and lith, and Dep also has its weight gain stories (though you could be one of the lucky ones with this -- probably different thngs triggered from lith).
Good luck and let us know how you go.
When I'm not in my right mind, my left mind gets pretty crowded...********************