Preheat oven to 350°F (175°C). Grease three 8-inch round cake pans and line the bottoms with parchment paper.
Place the unpeeled bananas on a parchment-lined baking sheet and roast in the preheated oven 20–25 minutes, until the skins are blackened. Remove and cool until easy to handle. Peel and mash the bananas in a bowl until mostly smooth; set aside.
In the bowl of a stand mixer or a large bowl with a hand mixer, beat together 1 cup canola oil, 1 cup plain Greek yogurt, 3 large eggs, 1 cup granulated sugar, 3/4 cup light brown sugar, 1 tablespoon vanilla extract, and 2 teaspoons lemon juice until combined and smooth.
Add the mashed bananas to the wet mixture and mix until evenly incorporated.
In a separate bowl, whisk together 3 1/2 cups all-purpose flour, 2 teaspoons baking soda, 1 teaspoon baking powder, and 1 teaspoon kosher salt. Add the dry ingredients to the wet mixture and mix on low speed just until combined—do not overmix.
Fold 1 cup shredded sweetened coconut into the batter with a spatula until evenly distributed.
Divide the batter evenly among the three prepared pans. Smooth the tops and bake at 350°F for 30–35 minutes, until the tops are set and a toothpick inserted into the centers comes out clean or with a few moist crumbs.
Remove the pans from the oven and let them cool in the pans for 5 minutes. Run a knife around the edges, invert each layer onto a cooling rack, remove the parchment, and allow the layers to cool completely before frosting.
Make the frosting: in a large bowl, beat 4 ounces cream cheese and 2 sticks butter (both at room temperature) until light and smooth, about 2 minutes.
Add 1 1/2–2 cups powdered sugar (start with 1 1/2 cups and add more to taste/desired stiffness), 1 cup unsweetened cocoa powder, and 2 teaspoons vanilla extract. Beat 2–4 minutes until the frosting is light and fluffy, adding the powdered sugar gradually if needed.
Beat in 1/2 cup canned coconut cream until fully incorporated. If the frosting is too soft to spread, chill 10–15 minutes and re-whip briefly.
Assemble the cake: place one cake layer on a serving plate, spread an even layer of frosting, repeat with the second and third layers, then frost the top and sides of the cake. Refrigerate the assembled cake, covered, for up to 2 days. Bring to room temperature before serving.