Is there any scientific research supporting the benefits of using herbs for Graves’ disease?

Yes,  Bugleweed (Lycopus virginicus or Lycopus europaeus-gypsywort) has been approved by German Commission E for use in mild hyperthyroidism. It is used in Europe for a mildly overactive thyroid, usually in the early stages and often with combination of Melissa. A study involving 62 patients confirmed positive effects of Bugleweed (Lycopus europaeus) in mild forms of hyperthyroidism without adverse reactions (1). German Bugleweed europaeus preparation is called Thyreogutt mono tablets or drops. Scientific studies of this preparation showed statistically significant improvements for mild hyperthyroidism for over 300 patients without side effects (2).

1.Beer AM, Wiebelitz KR, Schmidt-Gayk H. Lycopus europaeus (Gypsywort): effects on the thyroidal parameters and symptoms associated with thyroid function. Phytomedicine 2008 Jan;15(1-2):16-22.

2.Eiling R, Wieland V, Niestroj M. Improvement of symptoms in mild hyperthyroidism with an extract of Lycopus europaeus (Thyreogutt® mono). [Article in German]. Wien Med Wochenschr. 2013 Feb;163(3-4):95-101.