Whisk the milk, cream, and sugar together in a mixing bowl. Cover and put in the fridge for 30 minutes.
Set up your ice cream machine, leaving the frozen bowl in the freezer until it's time to use.
After the milk-sugar mixture is chilled, put your ice cream bowl on the ice cream machine.
Quickly mix your lemon juice and extract into the milk mixture and immediately pour into the ice cream machine.
Let the machine churn the ice cream until thick, but before it gets too thick (about 10 minutes in) add your diced lemon pieces, if using, bit by bit, to the churning ice cream. This keeps all of the pieces from getting gummed up in the bottom of the ice cream bowl.
Once churned, scoop into a freezable container and let ripen for at least 4 hours but preferably overnight.
After the ice cream is ripened and ready to serve, make or use pre-made Magic Shell to drizzle over scoops of ice cream. Garnish with sprinkles as desired and eat immediately.