1. Rinse rice well, and let drain in colander. Set aside.
2. Heat oil and butter in 2 quart saucepan on medium heat. Add onions and cook until brown. Remove from oil and drain on paper towels.
3. Add rice to remaining butter and oil, and cook until light brown, stirring frequently. Watch closely so it doesn't burn.
4. Add coconut milk, broth, onion, cinnamon, sugar. Bring to a boil, reduce to a simmer, and cook approximately 20 minutes stirring occasionally.
5. You may find the rice sticking to the pan, but scrape it up and stir it inches.
6. When rice is done, add the lime juice, turn off heat, and let sit for about 5 minutes. Stir and serve.