Boil 2 cups water in a medium sauce pan. Stir in rice and salt; bring to boil again.
Reduce heat to low. Cook covered, until water is absorbed and rice is soft, about 20 minutes.
Stir in dairy-free milk, cinnamon sticks, and lemon zest and increase heat. Cook for another 25 minutes, stirring occasionally to prevent sticking. Add coconut cream, sugar, and vanilla and cook for 5 more minutes.