Place the frozen raspberries, yogurt, orange juice, sugar, orange liqueur, vanilla extract, and salt into a blender. Process on high speed for 1 to 2 minutes until the mixture becomes completely smooth and creamy. Pause halfway through to scrape down the sides, ensuring all ingredients are thoroughly combined with no yogurt lumps remaining.

Set a fine-mesh strainer over a bowl and pour the blended mixture through it. Use the back of a spoon to press gently, extracting as much liquid as possible while capturing the seeds in the strainer. Once fully strained, add the lemon juice to the bowl and stir it through to brighten the flavor and add balancing tartness.

Place the strained mixture in the refrigerator or freezer for 10 to 15 minutes until it feels cold to the touch but hasn't begun to freeze solid. This step ensures the base is properly chilled for optimal churning and improved final texture.

Add the chilled mixture to your ice cream maker and churn following the manufacturer's directions, usually 20 to 25 minutes. Continue churning until the frozen yogurt reaches a soft-serve thickness—creamy, slightly fluffy, and barely firm enough to scoop.

For soft-serve texture, serve the frozen yogurt right away. For firmer scoops, transfer it to a freezer-safe container and freeze for 3 to 4 hours. Cover tightly with plastic wrap or an airtight lid to prevent ice crystals from developing on the surface.