Lithium can cause thyroid problems, but thyroid issues can cause mental health problems. A simple blood test can rule out thyroid issues. I know here everyone is screened for thyroid as it can mimick bipolar and anxiety.
My mother has thyroid problems, but I wonder if it was caused by the Lithium. Can Lithium cause thyroid problems?
Thyroid problems can cause mood-related symptoms. If you have hypothyroidism (underactive), it can seem like you're depressed. If you have hyperthyroidism (overactive), it can seem as though you're manic. My psychiatrist would always check my thyroid levels when I was first diagnosed to make sure it wasn't my thyroid or bipolar disorder aggravated by thyroid problems.
But as far as being related beyond a shadow of a doubt? Not really. You can have one without the other.
Regarding your query on whether bi-polar disorder and thyroid problems are related, I have never heard of bi-polar affecting the thyroid but I have heard that thyroid problems can affect bi-polar.
Thequietgirl makes a very good point, thyroid problems can be mistaken as mood swings, someone with an overactive thyroid could certainly give one of my hyper manic episodes a run for it's money, a friend had it and she struggled with the shakes and could run around non stop before they got the situation under control.
If you are not sent for a blood test to check your thyroid levels and you have any symptoms please make sure you request one. take care of yourself.