Beat the eggs with a whisk for 1-2 minutes until frothy. Stir in the sugar in stages and keep stirring until it has dissolved. Then stir in the cream and milk.
Finally stir in cinnamon and rum (not more than 2 tablespoon, otherwise the ice cream won`t freeze).
Freeze almost completely in the ice cream maker. Alternatively, put in a bowl and place in the freezer. Stir vigorously every hour to keep the ice cream creamy.
Puree the bananas and lemon juice. Just before the prepared ice cream is completely frozen, add the banana puree or stir in and let it freeze completely.