Study previous examples of dragon voices. The Sean Connery movie Dragonheart is an excellent example, as is The Two Towers, specifically the voice John Rhys-Davies uses for his lines as Treebeard. John Hurt's performance as the Great Dragon in the BBC series Merlin is also worth researching. All three have the same deep, precise delivery to their lines.
Before you begin to read, sit up straight with your shoulders wide, your head back and your feet placed on the floor. This opens your chest and allows you to breathe deeply. If desired, take a bite of a green apple or sip a glass of water to clear your throat.
Practice reading your lines and visualize your mouth dropping toward the floor as you speak. Your voice will drop as you do this and become deeper and slower. Breathe deeply and slowly as you talk as this will help lower your voice still further. Read through the lines two or three times before you actually perform them for an audience. This will give you an idea of their pace and make them sound more natural when you perform.