In a small bowl, combine the water, sugar, yeast, and stir to combine. Set it aside for about 5 minutes.
In a large bowl, add the flour and salt and mix to combine. Add the coconut milk, coconut oil, and the yeast mixture and stir together.
Once the dough comes together, take it out onto a clean surface to start kneading. Knead the dough for about 5 minutes until it becomes smooth. Shape it into a ball and put it in a clean, greased bowl and cover it to rise for an hour.
While the dough is rising, make the cinnamon filling. In a small bowl, combine the coconut oil, brown sugar, light brown sugar, ground cinnamon, and salt.
After the dough has risen, punch the dough in the bowl to deflate. Take it out onto a clean surface and roll it out into a 24 x 12 in / 60 x 30 cm rectangle. The dough should be spread out horizontally, with the long side facing you.
Spread the filling evenly on the surface, leaving about half an inch at the top. Starting from the bottom tightly roll the dough away from your body, toward the edge that has no filling, until you end up with a long log. Pinch the dough shut so the log doesn't unroll.
Cut the log into 12 equal pieces and place them in a parchment-lined 9 x 13 in / 23 x 33 cm baking pan. Cover and let the cinnamon rolls rise for 45 minutes. Once risen, bake in a preheated oven at 350°F / 180°C for 30 minutes. Take it out of the oven and let it rest for 20 minutes.
Take the remaining coconut milk and pour it into a small saucepan with the raw cashews. Heat the pan on medium heat until it reaches a boil, and turn the heat down. Simmer for about 12 to 15 minutes, until the coconut milk thickens.
Put the mixture into a blender along with the lemon juice and salt, and process until it becomes smooth. If it's too thick for the blender to process, add some nondairy milk, a teaspoon at a time.
Take the mixture out into a bowl and beat in the powdered sugar. Keep it in the fridge to chill and thicken, until ready to spread onto the cinnamon rolls and serve.