Prepare three 8-inch cake pans with parchment paper circles in the bottom and grease the sides of the pan.
Remove the lychees from the can with the syrup (saving the syrup for the frosting and the cake soak). Dry the lychees as much as possible, then dice them. Set aside.
In a large bowl, beat the sugar and oil together until well combined.
Beat in the eggs, coconut milk, and vanilla extract until the ingredients are well incorporated.
Mix in the flour, baking powder, and salt and beat until the batter is well combined and smooth, scraping down the sides as needed.
Add the chopped lychees to the batter and mix until incorporated.
Divide the batter evenly between the cake pans.
Bake in the preheated oven for 22-25 minutes, or until a toothpick comes out with a few crumbs. Let cakes cool.
In a small bowl, mix together the gelatin and water. Set aside.
Puree the strawberries using a blender or a food processor, set aside.
In a medium bowl, whisk together the egg yolks and sugar until the mixture turns pale and becomes thicker.
Place the egg and sugar mixture on top of a double boiler with simmering water underneath. Stir in the warm coconut milk, then stir the mixture over the double boiler until the yolk and milk mixture becomes thicker, about 4-5 minutes.
Remove the egg yolk mixture from the heat and whisk in the gelatin and strawberry mixtures until combined. Place this mixture into the freezer for 10-15 minutes to cool.
Meanwhile, use a mixer to whip the heavy cream until stiff peaks form.
Carefully fold the cooled strawberry mixture into the whipped cream in 2-3 installments, making sure not to deflate the cream. Add 1-2 drops of red food coloring if desired. Place the Bavarian cream in the fridge to set while you make the frosting.
Use a stand mixer or hand mixer to beat the butter until it is smooth and creamy.
Add in the powdered sugar, lychee syrup, and coconut milk and beat until frosting is smooth and fluffy.
Use a serrated knife to cut the tops off of the cooled cakes to make them flat.
Brush the tops of the cakes with a thin layer of lychee syrup.
Pipe a border of frosting around the edge of the bottom cake layer.
Spoon strawberry Bavarian cream into the center of the cake layer and spread until even. Top with the second cake layer and repeat.
Once the cake is built, spread the remaining coconut frosting on the tops and side of the cake and decorate as desired.