Wellbutrin tends to cause weight loss, and it's a crap shoot whether or not lithium will make you gain. I have never heard of a type of lithium that would make you less likely to gain, because lithium is about as simple as it gets, in the chemical sense. There are other bipolar drugs that are less likely to make you gain, but I don't think there's a difference between one brand of lithium and another (other than release time).
Are these the first meds they have tried for your treatment?