In a large saucepan, bring rice, water and salt to boil over medium high heat. Reduce heat to low, cover and simmer, until most of the liquid has been absorbed, about 15 minutes. Gently stir in rice milk, brown sugar, cinnamon sticks, and lemon zest ensuring mixture does not cook to the bottom of pan.
Increase heat to medium low, stirring often, until rice is tender and very creamy, about 40 minutes. Do not overcook or rice will be solid and not creamy when cooled. Rice pudding can be kept covered in the refrigerator for up to 5 days.
In saucepan, combine raspberries, figs, maple syrup and lemon zest. Heat over low heat until warmed through and sauce thickens slightly, about 10 minutes. Cover until ready to use.
Serve rice pudding warm or at room temperature topped with compote.