Preheat oven to 350 F. In a bowl, mix together all the crust ingredients. The mixture should look like dark sand. Press the dough into a baking sheet lined with parchment paper. Bake for 10 minutes until the edges are crispy (this does't need to be perfect, we will crust it up later). Let the pan cool for a couple minutes.
Next, break up the crust into small pieces and place them in a food processor (you can also crush them up by hand if you don't have a food processor). Add another 2 - 3 tablespoon coconut oil and pulse until the mixture looks like sand again. You should be able to press it together with a rubber spatula and it sticks together.
Place a piece of parchment paper in the bottom of a 9-spring form pan. Press the crust into the pan and up against the sides. Use a measuring cup to help push it up the sides. Place the crust back in the oven for another 8 minutes to bake. Let cool while you prepare the filling.
Reduce oven heat to 325 F. Place a 9 X 13 inch baking dish on the bottom rack of the oven. Prepare a pot on the stove with 6 cups of water and bring to a boil (this is called a "water bath" and will go into the baking dish when we're ready to bake the cheesecake).
In a mixing bowl, beat the cream cheese on low speed until it looks creamy with no clumps. You want to keep the mixer moving at low speed for the filling to reduce the likelihood of air bubbles. Add the coconut milk, maple syrup, vanilla, and lemon juice and mix again. Finally, add the arrowroot starch and mix to incorporate.
Pour the cheesecake filling into the crust. Level off the top with a rubber spatula. Open the oven door and pour the boiling water into the baking dish on the bottom rack. Then slide the cheesecake onto the middle rack of the oven. Try to do this step fairly quickly so you don't release too much heat from the oven. Bake for 1 hour and 10 minutes. To check if your cheesecake is done, open the oven door and gently push the cheesecake and watch how the filling moves. If it moves like a bowl of milk, it's not done. If it slightly jiggles (like jello) then it is done. Close the oven door back and turn off the oven. Keep the cheesecake in the oven for another hour until the oven cools down. This is done to gradually bring the cheesecake back to room temperature and prevent cracks. After an hour, remove the cheesecake and let it sit on the counter until it's complete at room temperature before transferring to the fridge.
To prepare the filling, place the cranberries, juice, and coconut sugar in a sauce pan on the stove over medium heat. Bring the mixture to a simmer. Once simmering, remove the pan from the element and let it cool down, it will also thicken up in this time. Once cool, spoon the cranberry mixture over the top of the cooled cheesecake.
When ready to eat, remove the cheesecake from the spring form pan, slice, and enjoy!