Preheat the oven to 375°. In a bowl, toss the rhubarb with 3/4 cup of the sugar and let stand for 15 minutes, stirring occasionally. In another bowl, toss the strawberries with the remaining 1/2 cup sugar and let stand for 10 minutes, stirring occasionally. Using a slotted spoon, transfer the rhubarb to the strawberries; discard any rhubarb juice. Add the cornstarch, lemon juice and vanilla to the fruit and stir well. Transfer the mixture to a 9-by-13-inch glass baking dish.