Combine milk, sugar, and butter in a saucepan and bring to a boil. Add semolina, and cook, stirring constantly, until the mixture thickens. Put the pudding in four 4-ounce cups that are rinsed with cold water and lightly sprayed with nonstick cooking spray.
Boil currants with the water, sugar, and lemon juice. Cook until the sugar is dissolved and the currants are very soft, about 10 minutes. Puree mixture in a blender and then push through a strainer to get a smooth sauce.
Refrigerate pudding and sauce until cold, about 2 hours. Unmold the pudding onto dessert plates and dress with sauce.