1Put the strawberries, raspberries, lemon juice and sugar in a saucepan. Stir over medium heat for 2 minutes until the sugar has dissolved. Bring to a boil. Boil gently for 3 minutes without stirring. Remove from the heat. Cool for 10 minutes.
2Pour the berry mixture into a blender or food processor and blend or process until smooth. Strain the mixture into a measuring cup, pushing the mixture through the sieve. Discard the solids remaining in the sieve. Cover and refrigerate for 2 hours until cold.
3Stir the berry mixture into the yogurt.
4Pour the chilled mixture into the ice cream bowl. Set the ice cream maker to the desired setting and churn.
5Once the yogurt is frozen transfer to a freezer-safe container, just large enough to contain the yogurt. Freeze for 3-4 hours or overnight for firmer yogurt.
6Scoop into bowls and serve.
7Store yogurt in the freezer for up to 2 weeks. The yogurt will become very firm after freezing overnight, so remove from the freezer and stand at room temperature for 5-10 minutes before serving for easier scooping.