Combine sugar and corn starch in a pan on the stove over medium heat. Gradually stir in the water until smooth.

Add berries and lemon juice. Bring to a boil, then reduce heat to low and simmer, uncovered, until slightly thickened.

Slightly mash the berries with a potato masher, or pour the whole mixture into a blender and puree. Strain if desired.

Let mixture cool before adding to ice cream.