Can 400mg lithobid (lithium carbonate) daily cause thyroid problems? Since my TSH before-after rise from 3, 2 to 14, 3 mlu/l.

Yes... It is not at all unusual for lithium to affect the thyroid and cause hypothyroidism, which is what it appears you are seeing with that increase in the tsh. If someone needs to stay on lithium, then the thyroid issue needs to be treated. See the dr prescribing your lithium who may want to refer you to your regular medical dr or an endocrinologist. It is not usually a reason to go off the lithium.