Prepare the frosting: Combine all of the ingredients (except for the lemon juice and vanilla extract/paste) in a medium size sauce pan. Whisk together then bring to a boil over high heat. Reduce to a simmer, cover and cook for 20 minutes, or until agar flakes have dissolved. Remove from heat and stir in vanilla extract and lemon juice. Transfer to a bowl, allow to cool, then cover and store in the refrigerator for at least 2 hours or up to overnight.
Once the frosting is firm, use a spoon to scoop it out into a food processor and then blend until smooth, scraping the sides with a spatula as needed. Add vanilla paste (if using) and blend until well-combined. Transfer the frosting from the processor back to the bowl and refrigerate again for at least 1-2 hours to allow it to firm up some more.
Prepare the cake: Preheat the oven to 350°F and grease an 8-inch round (or 9-inch square) cake pan. Combine the dry ingredients in a large bowl and set aside. In a separate medium size bowl, mash the banana along with the maple syrup, sugar, vanilla extract and coconut oil. Add the almond milk and lemon zest and whisk until smooth. If there are any large lumps from the banana, you can use the food processor to blend it until smooth.
Add the wet mixture to the dry then use a spatula to gently fold together until combined. Pour the batter into the cake pan then bake in the preheated oven for 25 minutes, or until you can prick the center with a fork and it comes out clean. Allow the cake to cool completely before frosting.
Once cake is properly cooled, spread the frosting on top. Serve immediately or refrigerate until ready to serve. Leftovers will stay good for up to 3 days in an airtight container in the refrigerator.