In a large bowl combine the diced strawberries with ⅓ cup sugar and lemon juice. Allow to refrigerate overnight, stirring once or twice.
In a medium bowl, beat the eggs until frothy, about 2 minutes. Add the coconut milk, milk and coconut cream and whisk well to combine. Pour the cornstarch, 2/3 cup sugar and salt into a saucepan; whisk well to combine. Add the egg mixture into the saucepan and whisk again. Cook over medium heat, whisking constantly for 5 to 7 minutes, until the mixture thickens. Remove from the heat and stir in the butter and vanilla. Let the pudding cool for a couple of minutes.
Strain the pudding through a fine sieve into a large bowl. Place plastic wrap directly on top of the pudding to prevent a film from forming. Refrigerate until ready to serve, at least 2 hours.
To assemble, place ½ cup of cake cubes in the bottom of a bowl. Spoon a ½ cup of the macerated strawberries and liquid over the cake cubes and allow to soak in. Top with ½ cup of the pudding to smoothly cover. Chill overnight or serve immediately, garnished with toasted coconut flakes, strawberry slices and mint leaves.