In a 3- to 4-quart pan, combine blueberries, raspberries, sugar, and lemon juice. Bring to a boil over medium-high heat, then reduce heat and simmer, stirring occasionally, until berries begin to disintegrate and mixture starts to thicken, about 15 minutes. Press through a fine strainer into a bowl, extracting as much liquid as possible with the back of a spoon or a spatula; discard seeds and skins.
Serve coulis warm; if mixture cools before you're ready to serve, reheat in a microwave oven. If it's too thick, stir in a little warm water.
