In a food processor, purée the banana with the lemon juice and vanilla until smooth. Set aside.
In a saucepan off the heat, combine the sugar and cornstarch. Add the eggs and combine with a whisk until smooth. Stir in the milk and puréed banana.
Bring to a boil, stirring and scraping the bottom of the pan. Simmer for about 5 seconds. Strain into a bowl and cover with plastic wrap directly on the pastry cream. Let cool and refrigerate for about 3 hours or until completely chilled.
In a saucepan, bring the water and sugar to a boil. Cook without stirring until the mixture turns an amber colour. Remove from the heat and gradually add the cream. Beware of splattering. Add the butter and bring to a boil, stirring until the sauce is smooth. Transfer to a bowl. Let cool. Cover and let cool to room temperature for about 3 hours.
In a bowl, whip the cream and sugar until semi firm peaks form.
In a 3 litres (12 cups) serving glass bowl, scatter a third of the cake cubes. Top with a quarter of the caramel sauce. Cover with a third of the pastry cream. Repeat two more times. Refrigerate until serving time. Garnish with the whipped cream and banana slices and drizzle with the remaining caramel.