Combine raspberries, sugar, water, and lemon juice in a saucepan over medium heat; cook and stir until raspberries break down, sugar dissolves, and sauce is heated through, 3 to 7 minutes. Do not overcook.
Remove from heat and press sauce through a fine-mesh strainer to remove seeds.
Cool to room temperature, cover the bowl with plastic wrap, and refrigerate until chilled, at least 45 minutes.
Notes
For thicker coulis, omit water. For thinner coulis, add 1-2 tablespoons water.