In a large measuring cup, combine the vanilla Greek yogurt, sugar, fresh lemon juice, and lemon zest. Whisk until smooth and creamy, about 2–3 minutes.

If you have an ice cream maker, pour the mixture into the chilled bowl and churn according to the manufacturer's instructions, typically for about 20–30 minutes.

If you don’t have an ice cream maker, pour the mixture into ice cube trays or a shallow dish and freeze until solid, about 4 hours.

Blend the frozen yogurt cubes in a blender or food processor for 1–2 minutes until smooth. Add a splash of milk if necessary.

Enjoy immediately for a soft-serve texture or transfer to an airtight container and refreeze for at least 1–2 hours for a firmer result.