Put the raspberries in the saucepan. Whisk together the sugar and arrowroot and add to the raspberries. Stir in the lemon juice juice and water and bring to a boil. Reduce heat and simmer while stirring until the berries break down and the sauce thickens, about 10 to 15 minutes. Remove from the heat and allow to cool. The sauce will continue to thicken as it cools.
Puree the sauce in a blender or with a handheld immersion blender, then strain it through a fine sieve. Serve warm or cold. The sauce will keep in the refrigerator for up to two weeks.