Is it safe to take a supplement containing 300 mg of l-tyrosine when I'm already treating my graves' disease with levothyroxine and methimazole?

Wasting your money. Who told you this is a good idea? Tyrosine is not an essential amino acid. Your body can make all the tyrosine it needs from phenylalanine, which IS an essential amino acid. All taking exogenous tyrosine does is reduce your requirement for phenylalanine. Any excess of either amino acid is burned as fuel or excreted. Don’t enrich the hucksters who make and sell the tyrosine.
Graves medications. L-tyrosine is an Amino Acid and also a precursor to thyroid hormone, l-thyroxine. It could stimulate further the hyperthyroidism of your graves. Not a good idea. Are you using the levothyroxine and Methimazole as directed by your endocrinologist? That combination is unusual, although not unheard of. One suppresses the thyroid, the other increases thyroid levels.