Begin by carefully slicing the tops off the clementines and scooping out the flesh, leaving behind a thin layer of membrane. Aim for soft, juicy segments and place them into a mixing bowl until you have about 3¼ cups once blended.

In a blender, combine the clementine flesh with a splash of lemon juice. If needed, add orange juice to bring the total liquid to 3¾ cups. Blend until smooth and creamy.

Transfer the blended mixture to a bowl, cover with plastic wrap, and chill in the refrigerator for at least 30 minutes.

Once chilled, pour the mixture into your ice cream maker and churn according to the manufacturer's instructions for about 20 to 30 minutes until it achieves a soft-serve consistency.

Serve the sorbet immediately for a soft texture or transfer it to an airtight container for later enjoyment.